APPLIED TIME SERIES ST 3009
Dr. N.D. Basnayake
BASIC OBJECTIVES OF TIME SERIES ANALYSIS
The basic objective usually is to determine a model that describes the pattern
of the time series.
Uses for such a model are:
1. To describe the important features of the time series pattern.
2. To explain how the past affects the future or how two time series can
“interact”.
3. To forecast future values of the series.
Overall Regular Repeating Erratic or
persistent periodic swings or residual
Long term fluctuations, movements fluctuations
movement usually within over more
a 12-month than one
period year
COMPONENTS OF TIME SERIES
COMPONENTS OF TIME SERIES
COMPONENTS OF TIME SERIES
IMPORTANT QUESTIONS TO ASK
Is there a trend, meaning that, on average, the measurements tend to increase (or
decrease) over time?
Is there seasonality, meaning that there is a regularly repeating pattern of highs
and lows related to calendar time such as seasons, quarters, months, days of the
week, and so on?
Are their outliers? In regression, outliers are far away from your line. With time series
data, your outliers are far away from your other data.
Is there a long-run cycle or period unrelated to seasonality factors?
Is there constant variance over time, or is the variance non-constant?
Are there any abrupt changes to either the level of the series or the variance?
Overall Regular Repeating Erratic or
persistent periodic swings or residual
Long term fluctuations, movements fluctuations
movement usually within over more
a 12-month than one
period year
CYCLIC AND SEASONAL TIME SERIES
Seasonal Pattern
• A seasonal pattern exists when a series is influenced by seasonal factors
(e.g., the quarter of the year, the month, or day of the week).
• Seasonality is always of a fixed and known period.
• Hence, seasonal time series are sometimes called periodic time series.
CYCLIC AND SEASONAL TIME SERIES
Seasonal Pattern (Example)
CYCLIC AND SEASONAL TIME SERIES
Seasonal Pattern (Example)
CYCLIC AND SEASONAL TIME SERIES
In a seasonal pattern there is a
precise amount of time between
the peaks and troughs of the
data.
Cyclical behavior on the other
hand can drift over time
because the time between
periods isn't precise
CYCLIC AND SEASONAL TIME SERIES
Cyclic Pattern
A cyclic pattern exists when data exhibit rises and falls that are not of fixed
period. The duration of these fluctuations is usually of more than one year.
In general, the average length of cycles is longer than the length of a
seasonal pattern,
and
the magnitude of cycles tends to be more variable than the magnitude of
seasonal patterns.
INTERPRET THE TIME SERIES PLOT
INTERPRET THE TIME SERIES PLOT
INTERPRET THE TIME SERIES PLOT
TIME SERIES DECOMPOSITION
Time Series
Components
Trend Cycle Seasonal Random
(Remainder)
Trend + Cycle (Trend)
TIME SERIES DECOMPOSITION
ADDITIVE SEASONALITY
The additive decomposition is the most appropriate if the magnitude of the
seasonal fluctuations, or the variation around the trend-cycle, does not vary
with the level of the time series.
MULTIPLICATIVE SEASONALITY
When the variation in the seasonal pattern, or the variation around the trend-
cycle, appears to be proportional to the level of the time series, then a
multiplicative decomposition is more appropriate. Multiplicative
decompositions are common with economic time series.
ADDITIVE VS. MULTIPLICATIVE
EXAMPLES
EXAMPLES
THANK YOU!
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