Manual

EViews 4.0

By

Christian Nagstrup

Description IT-Department

Basic insight into EViews Ver. 021120

 TABLE OF CONTENTS

INTRODUCTION ..................................................................................................................................1
1 EVIEWS FILES AND DATA........................................................................................................1
1.1 CREATING A WORKFILE .............................................................................................................1
1.2 IMPORTING TIME SERIES DATA FROM EXCEL .............................................................................2
1.3 TRANSFORMING THE DATA ........................................................................................................7
1.4 CREATING SEASONAL DUMMY VARIABLES ................................................................................8
1.5 COPYING OUTPUT ......................................................................................................................9
2 EXAMINING THE DATA ............................................................................................................9
2.1 DISPLAYING LINE GRAPHS .........................................................................................................9
2.2 DRAWING A SCATTER PLOT .....................................................................................................10
2.3 OBTAINING DESCRIPTIVE STATISTICS AND HISTOGRAMS .........................................................11
2.4 DISPLAYING CORRELATION AND COVARIANCE MATRICES .......................................................12
3 ESTIMATING EQUATIONS .....................................................................................................12
4 TESTING FOR UNIT ROOTS ...................................................................................................15
5 ARIMA IDENTIFICATION AND ESTIMATION...................................................................18
6 USING EVIEWS COMMANDS .................................................................................................21
6.1 INTERACTIVE USE ...................................................................................................................21
6.2 BATCH PROGRAM USE ............................................................................................................22
7 WORKING WITH MATRICES.................................................................................................22
7.1 DECLARARING MATRIX OBJECTS .............................................................................................23
7.2 ASSIGNING MATRIX VALUES ..................................................................................................24
7.3 MATRIX OPERATORS ...............................................................................................................25
7.4 MATRIX COMMANDS AND FUNCTIONS .....................................................................................27
7.4.1 Transposing a matrix object ...........................................................................................28
7.4.2 Calculating the rank .......................................................................................................28
EViews Manual November 2002

Introduction

EViews is an econometrics package, which provides data analysis, regression and

forecasting tools. EViews can be useful for many different analyses, but this
introduction will focus on financial analysis. Once you get familiar with EViews, the
program is very user-friendly. Unlike Microsoft Excel, however, EViews is not a
spreadsheet program, and this can cause a few problems in the beginning. In the next
section we will look at how to avoid such problems. At the same time it is worth
mentioning that EViews has an excellent help function, where you can seek additional
assistance.

1 EViews Files and Data

The following sections describe how to create a new workfile and import data into
EViews. Different ways of handling the data in the workfile are shown as well.

1.1 Creating a workfile

Before you carry out any analysis you must first create a so-called workfile, which
must be of the exact size and type as the data you want to work with. After the
workfile is created EViews will let you import files from Excel, Lotus, ASCII (text
files) etc. Data from SAS or SPSS cannot be directly imported to EViews. Instead the
data must be saved as a text file before importing1. Entering data directly into EViews
can be done, but is generally easier to do this in Excel first.

To create a workfile click File → New → Workfile and the following dialog box will
appear:

1
The SPSS manual includes a description of this procedure. For SAS you can refer to the student
instructors at the IT-Department.

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If you are working with time series data you need to know the sampling period (daily,
monthly, quarterly etc.) as well as the starting and finishing date for the data. If you
are working with cross-sectional data you need the number of observations. So in the
latter case you should choose Undated or irregular and enter the start observation and
the end observation in the appropriate textboxes. We will now look at an example
where time series data is imported from an Excel file using the import function2. It
can be done by copy-and-paste as well, which is described in EViews’ help function.

1.2 Importing time series data from Excel

The file we would like to import (X:\Eviews\Eviews_ex1.xls) can be viewed below.

2
The procedure for importing text files is very similar and will therefore not be demonstrated here.

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The following 5-step procedure for importing time series data can be used:3

1) Examine the contents of the file in Excel and note

- the start and end date of the observations
- the cell where the data starts (usually B2)
- the names of the variables and the order in which they appear
- the sheet name

This example has daily (5 day weeks) data with a start date of 01-01-1998 and an end
date of 31-12-1998. The data starts at B2 in the sheet called Sheet1. There are 11
variables. Some of them have very long names so it will be a good idea to change
these to make them easier to work with later.

2) Create a new workfile as described above.

3
For cross-sectional data you note the number of observations in the dataset instead of the start and end
dates. This should be the only difference.

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You should choose Daily [5 day weeks] and enter 01/01/1998 as the start date and
12/31/1998 as the end date. Be aware of the American format, MM/DD/YYYY. In the
case of quarterly data you would enter 1975:3 e.g. for the third quarter of 1975.
Monthly data follows the same pattern, i.e. 1975:1 means January 1975 and 1975:3
means March 1975. After clicking OK you should end up with the workfile shown
below.

The range as well as the sample is the period between 01-01-1998 and 31-12-1998.
There are always two different series, C and RESID, as default. C is the column that
will contain the coefficients from the last regression equation you have estimated.
RESID is the column that will contain the residuals from your last estimated model.

3) Click Procs → Import → Read Text-Lotus-Excel. In the dialog box for Open
choose the Excel format and browse for the file. Select the file and click Open.

NB!! Remember to close the file in Excel before you try to

import it to EViews. Otherwise there will be an error message.

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4) A dialog box now appears in which it is very crucial to enter the correct
information. Any mistakes could result in an incomplete or even wrong dataset. This
is where our former check-up of the Excel file becomes very important.

In this example the dialog box should be filled out as follows:

The order of data is (as in most cases) By Observation – series in columns. Upper-left
data cell is B2 and the sheet name is Sheet1. If there is only a single sheet (as in this
example) it is not necessary to enter the name of it.

The names of the series/variables have been changed (notice that no spaces are
allowed in the names) in order to make them easier to work with. However, if you
would like to import the names that are given in Excel you simply enter the number of
series (in this case 11). These names can then be changed in EViews using the
Rename function. However, using this method can cause problems if for example the
names start with a number and are very similar (e.g. names such as 7 DAY RETURN,
30 DAY RETURN etc.).

The sample to import is taken from the workfile. Here it is possible to exclude
periods, which can be useful in case you would like to get rid of any outliers.

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The workfile that you should have by now is shown below.

It contains a list of the 11 imported variables in alphabetical order as well as the two
columns for the estimated coefficients and the residuals. It is always a good idea to
check if the first and the last imported variables have been correctly imported4. In this
example you do this by double clicking STOCK_A and RF180 and compare these
series with the Excel file.

Another useful approach is to open the two variables as a group. You do this by:
- clicking the variable STOCK_A
- holding down the [Ctrl] key and clicking the variable RF180
- clicking View → Open as One Window → Open Group
or simply just right clicking or double clicking on either of the selected
series and then clicking Open Group

4
Common errors include rows with “NA” and numbers that are too high or low (if the decimal
separator has been misinterpreted – for instance 43500 instead of 435,00).

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5) If you are certain that you have imported the data into the EViews workfile
correctly you should now save this workfile by clicking File → Save As. The
workfile will be saved in EViews’ own ‘.wf1’ format. A saved workfile can be
opened later by selecting File → Open File → Workfile from the main menu.

1.3 Transforming the data

It is often useful to transform existing variables for various purposes. This can be
done in EViews using the [Genr] button in the top right hand corner of your workfile.
Say you would like to find the return on STOCK_A in the X:\Eviews\Eviews_ex1.wf1
workfile. The continuous return can quickly be calculated by means of the DLOG
function. This finds the difference between the log of the current price and the log of
the previous price; ln( Pt ) − ln( Pt −1 ) . Simply click the [Genr] button and enter the

equation below followed by OK.

This will create the variable RET_A and include it in the workfile. You can view the
returns by double clicking the variable.

Besides DLOG there are naturally a number of other mathematical functions as well
as simple addition, subtraction, division and multiplication available. A useful one
worth mentioning here as well is the lag function. Lagging a variable is simply done

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by entering the name of the followed by (-k), where k is the number of lags. So if you
would like to calculate the first difference for the variable STOCK_B for example, you
create the following variable:

If you need the lagged variable in a regression model for example, you could simply
enter the variable STOCK_B(-1) in your equation.

1.4 Creating seasonal dummy variables

We will demonstrate how to create such dummy variables by assuming that we have a
workfile containing quarterly data for the period 1975:1 (first quarter of 1975) to
2000:4 (fourth quarter of 2000). To create a dummy variable (named Q4) with 1’s in
the fourth quarter of each year and 0’s in other quarters, you click the [Genr] button
in your workfile and enter the following equation:

Q4 = @SEAS(4)

If you are working with monthly data, the number in the bracket refers to months
instead. So if you for example would like to test for the ‘January effect’ on the stock
market you could create a dummy variable (named JAN), which has a value of 1 in
January each year and 0 in the remaining months. JAN is created by entering the
following equation:

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JAN = @SEAS(1)

If you wish to create a dummy variable to model the impact of the stock market crash
of October 1987 in your fictive workfile with monthly data, you can follow this quick
procedure: Click the [Genr] button in your workfile and enter the equation DUM1987
= 0. When the new dummy variable is created you click the [Genr] button again. This
time you change the sample from [1975:1 2000:4] to [1987:10 1987:10] (i.e. October
1987 only) and enter the equation DUM1987 = 1. The variable DUM1987 now
contains a value of 1 in October 1987 and 0 values in all other months.

1.5 Copying output

Any graph or equation output can easily be copied into a Word document for
example. To copy a table, simply select the area you want to copy and click Edit →
Copy. A dialog box should appear, where you would usually select the first option:
Formatted – copy numbers as they appear in table. Then you go to Word and paste
the selected area and change the size of the output until it suits your document.

To copy a graph, click on it and a blue border should appear, then click Edit → Copy.
In the appearing dialog box, click Copy to Clipboard and then paste into Word. Again
the size can be adjusted to a suitable size.

2 Examining the data

EViews can be used for examining the data in a variety of ways. In the following a
few will be demonstrated.

2.1 Displaying line graphs

If you want to select a few variables and display a line graph of each of the series, you
can follow this example based on the workfile X:\Eviews\Eviews_ex1.wf1.

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In this example we want to view the first three time series in the workfile, STOCK_A,
STOCK_B and STOCK_C. The procedure is to highlight the three variables (using the
mouse and the [Ctrl] key) followed by a double or right click. Then you click Open
Group and click the [View] button in the appearing spreadsheet. From this menu you
click Multiple Graphs → Line and the three line graphs depicted below appear. As
you can see there are other choices of graphs as well. In general, clicking the [View]
button mentioned above offers you many options of viewing your selected data.

If you want to save the output in your workfile for later use, you first click the
[Freeze] button. In the new window which appears you click the [Name] button. In
the dialog box you enter a name for the output and click OK. Now the output appears
with a graph icon in your workfile.

2.2 Drawing a scatter plot

The procedure is similar to the one just mentioned above, but when using scatter plots
in connection with a regression model it is now important to highlight the independent

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variable first, and then hold the [Ctrl] key and click the dependent variable. This
secures that a regression line will be correctly drawn.

We can show an example from our workfile (X:\Eviews\Eviews_ex1.wf1) where

STOCK_A is plotted against MAR_IND. In a regression model we want STOCK_A to
be the dependent variable and MAR_IND to be the dependent variable. Consequently
we first highlight MAR_IND followed by the other variable. Double click and choose
Open Group in order to open a spreadsheet with the two variables. Click the [View]
button and choose Graph → Scatter → Scatter with Regression. A dialog box will
now appear. For default values just click OK and the scatter plot shown below should
appear. If you only need a simple scatter plot just choose Simple Scatter instead. To
save the output in your workfile use the same procedure as described in section 2.1.

2.3 Obtaining descriptive statistics and histograms

You can obtain a histogram and the descriptive statistics of a series by double clicking
the series in the workfile. In the appearing spreadsheet you click the [View] button
and choose Descriptive Statistics → Histogram and Stats.

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If you want to obtain descriptive statistics for several series at a time instead, you
highlight the relevant series (using the mouse and the [Ctrl] key), double or right click
and choose Open Group. In the appearing spreadsheet you click the [View] button
and choose Descriptive Statistics → Individual Samples. This procedure will not
give you the histograms, however.

Again the procedure from section 2.1 can be used if you wish to save the output in
your workfile.

2.4 Displaying correlation and covariance matrices

The easiest way to display correlation and covariance matrices is to highlight the
relevant series (using the mouse and the [Ctrl] key) and then click Quick → Group
Statistics → Correlations (or Covariances if you want a covariance matrix). This
creates a new group and produces a common sample correlation/covariance matrix. If
a pair wise correlation/covariance matrix is more suitable (see the box below), this is
produced by clicking the [View] button and choosing Correlations (or Covariances)
→ Pairwise Samples.

NB!! If you have a matrix with several series/variables you should

be aware of any missing variables. If one of the series has missing
variables, then all the calculated cross-correlations will be different
from obtaining pair wise correlations instead!!!

Section 2.1 describes how to save your output in the workfile.

3 Estimating equations

In the following we will demonstrate how you estimate a regression model in EViews.
The example is based on the workfile X:\Eviews\Eviews_ex1.wf1.

When you have opened your workfile you click on the [Objects] button. Select New
Object → Equation and the following dialog box should appear.

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Alternatively, you could have clicked Quick → Estimate Equation.

Say we want to estimate the regression equation that is illustrated in the scatter plot
from section 2.2, i.e. we want STOCK_A as the dependent variable and MAR_IND as
the independent variable.

You can enter the model in two ways (of which the first is probably the quickest):

1) List

First you list the dependent variable followed by C for the intercept term and then the
independent variable(s). There must be a single space between each variable. In this
example we only have a single independent variable, so we will enter the following
simple regression into the first window:

STOCK_A C MAR_IND

2) Formula

In the same window you type the model as a true equation, where each coefficient is
written as C(k) with k = 1, 2, 3, …. In our simple regression example we would enter:

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STOCK_A = C(1) C(2)*MAR_IND

When you have entered your preferred equation you select the estimation method
(default is Least Squares) and your sample (default is the entire sample). The
[Options] button gives you the opportunity to change the estimation procedure
further. For example you can choose the White correction or the Newey-West
correction if the dataset has problems with heteroscedasticity. To do this you simply
check the [Heteroscedasticity] button and select either White or Newey-West. The
help function in EViews provides a more detailed discussion of these corrections.

In this example we will not make any corrections, so we just click OK and get the
following output.

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This output is obtained by using the List method and is slightly different from the
output resulting from the Formula method. However, the interpretation is exactly the
same.

If you want to save the regression model that you have estimated in your workfile you
simply click the [Name] button above the output. Enter a name and click OK.

It is also possible to re-estimate an equation by clicking the [Estimate] button. The

previous Equation Specification dialog box re-appears and you can make any
preferred changes. For example you can include more independent variables or
exclude any outliers in the Sample window.

4 Testing for unit roots

Testing for unit roots is useful when you want to know whether a time series is
stationary or not. A time series is stationary if and only if |ρ| < 1 in the following
regression model:

Xt = µ + ρXt-1+εt

Therefore, you have to test whether or not ρ = 1. If ρ ≥ 1 then ρ does not follow a
standard distribution and consequently the usual t-test is not valid. The ρ-coefficient
will therefore be tested against the so-called Dickey-Fuller distribution, which is used
to test for stationary time series.

This test is quickly done in EViews by double clicking the relevant time series in
order to go to the spreadsheet view. Here you click the [View] button and select Unit
root test. The following dialog box should appear.

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In the dialog box you first select the test type. In this example we will use Augmented
Dickey-Fuller5. Next you select whether you want to test for unit root in:

Level (Xt )
1st difference (Xt-Xt-1=∆Xt)
or 2nd difference (∆Xt-∆Xt-1).

Furthermore, you are asked whether you want to include other exogenous variables in
the test equation. You can choose between the following:

k
1. ∆X t = µ + γX t −1 + ∑ δ i ∆X t −i + ε t (Intercept)
i =1

k
2. ∆X t = µ + γX t −1 + βT + ∑ δ i ∆X t −i + ε t (Trend and intercept)
i =1

k
3. ∆X t = γX t −1 + ∑ δ i ∆X t −i + ε t (None)
i =1

As you can see, a number of lagged first differences of the test variable are included
in the test regression. The exact number is specified in the Lagged differences
window.

5
For a short description of the theory behind the Augmented Dickey-Fuller and Phillips_Perron tests
you can refer to the help function in EViews, which provides references to more detailed sources as
well.

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You can decide which of the models to estimate from looking at a plot of ∆Xt. From
this plot you estimate if the time series has a mean different from zero (model 1), if
there is a trend in the time series (model 2), or if the time series has a mean around
zero (model 3).

In the output below you see a plot of the short interest rate in Denmark, KORT_DK
(The plot is obtained by double clicking the variable, clicking the [View] button and
selecting Graph → Line).

We will test to see whether the time series is stationary around a mean different from
zero, i.e. model 1 above. You can see the output from this test below.

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You see the ADF test statistic to the left (-2.043879) and the critical values to the
right. The hypotheses are the following:

H0 : ρ = 1 (non-stationary time series)

H1 : ρ < 1 (stationary time series)

The null hypothesis of a unit root is rejected against the one-sided alternative if the
test statistic is less than (lies to the left of) the critical value6. In this example, the test
fails to reject the null hypothesis of a unit root in the time series at all three levels of
significance. Therefore, it is not possible to reject that the time series is non-
stationary.

5 ARIMA identification and estimation

The identification of an ARIMA model is done by examining a correlogram. In

EViews you obtain a correlogram for at variable by double clicking the variable to
open the spreadsheet view. Here you click the [View] button and choose
Correlogram. In the appearing dialog box you choose between level, first difference,
or second difference and then you enter the desired number of lags to include. An
example of a correlogram for the variable INDEX is shown below.

6
If ρ > 1 the series is said to be explosive (and consequently does not make much economic sense).
Therefore it is not included in the alternative hypothesis.

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An ARIMA estimation consists of four steps, or the so-called Box-Jenkins

methodology for ARIMA models (Madsen (1992), pp. 101-115 & Maddala (1992),
pp. 542-543)7:

1) Identification
2) Estimation
3) Diagnosis
4) Forecast

In step 1 you compare the estimated autocorrelations for the residuals with the
theoretic autocorrelations, which normally arise in a given ARIMA model. If there are
any autocorrelations between the residuals, it is possible to set up an ARIMA model.
Examining the nature of the correlation between the residuals is useful in determining
p and q in the AR (autoregressive) and MA (moving average) components.

7
Madsen, Henning (1992), ”Forecasting Economic Time Series An Introduction”, Institut for
Informationsbehandling, Handelshøjskolen i Århus.
Maddala, G. S. (1992), “Introduction to Econometrics”, 2nd edition, Prentice Hall.

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From the correlogram above you see the plots of the serial autocorrelations (SACF)
and the partial autocorrelations (PACF). SACF is geometrically declining, but it is not
a long, linearly declining sequence. PACF is curtailed after lag 1. From the table
below you can see which ARIMA model fits this description.

Identification of ARIMA models using SACF and PACF

Process SACF PACF
AR (p) Geometrically declining Curtailed after lag p
MA (q) Curtailed after lag q Geometrically declining
ARMA (p,q) Declining after lag q Declining after lag p
If SACF shows a linearly declining sequence you should consider differencing the series.
Source: (Madsen (1992), p. 103)

According to the table, this example can be considered an AR(1) model. The SACF
and PACF characteristics do not suggest including a MA component or differencing
the series.

In step 2 you should estimate the identified ARIMA model. If an ARIMA model
includes a MA component you cannot use OLS estimation, as the model is non-linear.
Instead, a non-linear least squares estimation must be carried out. In this example
there is no MA component and common OLS estimation is therefore correct.
The model for an autoregressive process of order 1 can be written as:

(a) X t = α + ϕ 1 X t −1 + ε t

Model (a) can be transformed into:

(b) X t − µ 0 = µ + ϕ 1 ( X t −1 − µ 0 ) + ε t

Model (b) suggests that the time series is fluctuating around a mean. EViews allows
you to parameterise such a model yourself by using the command line interface (see
next section).

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6 Using EViews commands

So far we have only looked at the Windows interface of EViews. However, EViews
provides you with a command line interface as well. This is useful if you want to
create macros or work with matrices for example. Commands may be used
interactively, or executed in batch mode. Virtually every operation that can be
accomplished using menus may also be entered into the command window of EViews
or placed in programs for batch processing. For specific commands you can refer to
the EViews help function.

6.1 Interactive Use

To work interactively, you should type a command into the command window, then
press ENTER to execute the command immediately. If you enter an incomplete
command, EViews will open a dialog box prompting you for additional information.

The command window is located just below the main menu bar at the top of the
EViews window. The blinking vertical insertion bar at the left end of the command
window indicates that EViews is expecting a command.

A command that you enter in the window will be executed as soon as you press
ENTER. The insertion point need not be at the end of the command line when you
press ENTER. EViews will execute the entire line containing the insertion point.

As you enter commands, EViews will create a list in the command window. You can
scroll up to an earlier command, edit it, and hit ENTER. The modified command will
be executed again. You may also use standard Windows copy-and-paste between the
command window and any other window. The contents of the command area may
also be saved directly into a text file for later use. To do this you first make certain
that the command window is active by clicking anywhere in the window, and then
select File→ Save As… from the main menu.

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6.2 Batch Program Use

You can assemble a number of commands into a program, and then execute the
commands in batch mode. Each command in the program will be executed in the
order that it appears in the program. Using batch programs allows you to make use of
macro processing for example.

One way to create a program file is to select File → New → Program. EViews will
open an untitled program window into which you may enter your commands. You can
save the program by clicking on the [Save] or [SaveAs] button, browsing to the
desired directory, and entering a file name. The file name you enter will be given the
extension ‘.prg’.

Alternatively, you can use any (ASCII) editor to create a program file containing your
commands. The commands in this program may then be executed in EViews.

7 Working with matrices

EViews provides you with tools for working directly with data contained in matrices
and vectors. To make use of these tools it is required that you are familiar with the use
of EViews commands, which was discussed in section 7.

The following six objects (all called matrix objects) can be created and manipulated
using the matrix command language:

‰ Coef: column vector of coefficients to be used by Equation, System, Pool,

and Sspace objects
‰ Matrix: two-dimensional array
‰ Rowvector: row vector
‰ Scalar: scalar
‰ Sym: symmetric matrix (stored in lower triangular form)
‰ Vector: column vector

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7.1 Declararing matrix objects

All matrix objects must be declared prior to use. This declaration consists of the
object keyword followed either by size information (in parentheses) and the name to
be given to the object, or by the name and an assignment statement (e.g. matrix_a =
matrix_z).

The various matrix objects require different sizing information. A matrix requires the
number of rows and the number of columns. A sym requires that you specify a single
number representing both the number of rows and the number of columns. A vector,
rowvector, or coef declaration requires the number of elements. Of course a scalar
requires no size information. If no size information is provided, EViews will assume
that there is only one element in the object. If no assignment statement is included in
the declaration, EViews will initialize all values to zero.

Example:
Look at the following commands:

matrix(3,10) mat_a
sym(9) sym_x
vector(11) vec_y
rowvector(5) rvec_z

These four commands create a 3x10 matrix called mat_a, a symmetric 9x9 matrix
sym_x, an 11x1 column vector vec_y, and a 1x5 row vector rvec_z. All of these
objects are initialized to zero, since they have been given no assignment statements.

To change the size of a matrix object, you can repeat the declaration statement with
the new size information. Furthermore, if you use an assignment statement with an
existing matrix object, the target will be resized as necessary. Consider this example.

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Example:
Writing the commands

sym(10) big_z
matrix mat_a
matrix(10,2) mat_a
mat_a = big_z10

will first declare mat_a to be a matrix with a single element, and then redeclare mat_a
to be a 10x2 matrix. The assignment statement in the last line will resize mat_a so that
it holds the contents of the 10x10 symmetric matrix big_z.

7.2 Assigning Matrix Values

There are three ways to assign values to the elements of a matrix. In the following
only one of them will be demonstrated; the method of fill assignment. This should be
sufficient for most operations, but you can refer to the EViews help function if you
would like to know about the other two methods.

The procedure involves assigning a list of numbers to each element of the matrix in
the specified order. By default, the procedure fills the matrix column by column, but
you may override this behavior. You should enter the name of the matrix object,
followed by a period, the fill keyword, and then a comma delimited list of values.

Example:
The commands

vector(3) v
v.fill 0.1, 0.2, 0.3
matrix(2,4) x
x.fill 1, 2, 3, 4, 5, 6, 7, 8

create the matrix objects

 0 .1 
X = 
1 3 5 7
V =  0.2  and
 0 .3  2 4 6 8 
 

If we replace the last line with

x.fill(b=r) 1,2,3,4,5,6,7,8 (default is b=c, where c is colums)

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then X is given by

X = 
1 2 3 4
5 6 7 8 

In some situations, you may wish to repeat the assignment over a list of values. You
may use the l option to fill the matrix by repeatedly looping through the listed
numbers until the matrix elements are exhausted. Thus,

Example:
The commands

matrix(3,3) y
y.fill(l) 1, 0, -1

will create the matrix

1 1 1
Y = 0 0 0
−1 −1 − 1


7.3 Matrix Operators

EViews provides standard mathematical operators for matrix objects. With the
exception of comparison operators8, these will be discussed below.

Negation

The unary minus changes the sign of every element of a matrix object, yielding a
matrix or vector of the same dimension. If you for example want to change the sign of
the elements from a matrix, pos_x, you create the new matrix, neg_x, by typing:

matrix neg_x = -pos_x

8
Comparison operators are: =, >, >=, <, <=, <>. You can refer to the EViews help function for details.

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Addition and subtraction

You can add or subtract two matrix objects of the same type and size by using the
procedure in the following example.

Example:
If we consider the two matrices, a and b, created by the commands

matrix(3,4) a
matrix(3,4) b

then we simply add them by creating a new matrix called sum:

matrix sum = a+b

If you want to subtract the two matrices instead you just create another matrix:

matrix diff = a–b

As you can see we have called this new matrix diff.

You can add a square matrix and a sym of the same dimension. The upper triangle of
the sym is taken to be equal to the lower triangle. Adding a scalar to a matrix object
adds the scalar value to each element of the matrix or vector object. Similarly,
subtracting a scalar object from a matrix object subtracts the scalar value from every
element of the matrix object.

Multiplication

You can multiply two matrix objects if the number of columns of the first matrix is
equal to the number of rows of the second matrix.

Example:

matrix(5,9) a
matrix(9,22) b
matrix prod = a*b

The two matrices, a and b, are multiplied and the result is contained in the new
matrix, prod, which will have 5 rows and 22 columns.

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You use the same procedure when multiplying vectors, rowvectors, scalars and
combinations of all matrix objects. Another example can be considered.

Example:

rowvector(4) rv_a
rv_a.fill 2,3,0,1
matrix(4,4) mat_z
mat_z.fill 2,1,0,0,2,1,2,1,1,0,0,2,0,1,3,1
rowvector rv_res = rv_a*mat_z

Here the rowvector, rv_a, is multiplied with the matrix, mat_z. This should result in
the following rowvector:

RV_RES = (7 8 4 4)

Division

You can divide a matrix object by a scalar. Consider the following example.

Example:

matrix(2,3) orig
orig.fill 2,4,8,18,6,4
matrix div = orig/2

Each element of the matrix, orig, will be divided by 2. Thus we get the following
matrix:

1 4 3 
DIV =  
 2 9 2

7.4 Matrix commands and functions

EViews provides a number of commands and functions that allow you to work with
the contents of your matrix objects. Each is well described in the EViews help
function, and we will therefore only demonstrate a few basic ones in the following.

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7.4.1 Transposing a matrix object

The syntax @transpose(x) forms the transpose of a matrix object, x.

Example:
The following syntax

matrix(2,3) mat_a
mat_a.fill 4,2,5,7,0,4
matrix tr_a = @transpose(mat_a)

first creates the matrix, mat_a, and returns the transpose of mat_a in a new matrix:

 4 2
 
TR _ A =  5 7 
 0 4
 

7.4.2 Calculating the rank

The syntax @rank(x, n) returns the rank of a matrix object, x. The rank is calculated
by counting the number of singular values of the matrix which are smaller in absolute
value than the tolerance, which is given by the argument n. If n is not provided,
EViews uses the value given by the largest dimension of the matrix multiplied by the
norm of the matrix multiplied by machine epsilon (the smallest representable
number).

Example:

matrix(2,2) mat_x
mat_x.fill 1,2,1,2
scalar rank_a = @rank(mat_x)

Here the rank of mat_x is calculated and returned as a scalar, rank_a. You can view
the value of this scalar by double clicking it in your workfile. The value should appear
in the bottom left corner, and in this case it should equal 1.

Other basic commands include:

- @trace (returning the trace of a square matrix or sym)

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- @det (returning the determinant of a square matrix or sym)

- @inverse (returning the inverse of a square matrix or sym)
- @identity (creates an identity matrix)
- etc.

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