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Forecasting Crime Using ARIMA Model

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DOI: 10.48550/arXiv.2003.08006

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 Forecasting Crime Using ARIMA Model
Khawar Islam, Akhter Raza
1
Computer Science, Federal Urdu University, University Road Karachi, Karachi, Sindh,
Pakistan, E-mail: khawarislam@fuuast.edu.pk

Abstract
Data mining is the process in which we extract the different patterns and useful
Information from large dataset. According to London police, crimes are immediately
increases from beginning of 2017 in different borough of London. No useful
information is avail- able for prevent crime on future basis. We forecasts crime rates in
London borough by extracting large dataset of crime in London and predicted number of
crimes in future. We used time series ARIMA model for forecasting crimes in London.
By giving 5 years of data to ARIMA model forecasting 2 years crime data.
Comparatively, with exponential smoothing ARIMA model has higher fitting values. A
real dataset of crimes reported by London police collected from its website and other
resources. Our main concept is divided into four parts. Data extraction (DE), data
processing (DP) of unstructured data, visualizing model in IBM SPSS. DE extracts
crime data from web sources during 2012 for the 2016 year. DP integrates and reduces
data and give them predefined attributes. Crime prediction is analyzed by applying some
calculation, calculated their moving aver- age, difference, and auto-regression.
Forecasted Model gives 80% correct values, which is formed to be an accurate model.
This work helps for London police in decision-making against crime.
Key words: Data mining, Prediction, ARIMA model, Forecasting, Crime analysis.

1 Introduction
Crime is an activity or unpredictable scene against society. The increase of population
directly effects on country resources where government responsibility is to manage re-
sources allocating resources on right place. Crime is an activity which faces all
developing and developed countries [1]. Many techniques are applied to analyze crime
patterns and identify places where chances of crimes are maximum in the future. Some
crimes
∗
Corresponding author.
†
E-mail: khawarislam@fuuast.edu.pk

1
 Forecasting of future crime using Data Mining technique 2

applications are implemented and followed by the government [10]-[11]-[20]. Here, we

consider and dis-cuss the data mining technique for prediction with the availability of
different datasets, many researchers and experts used this datasets foe future prediction.
Many predictions are may be accurate or not depend upon the situation. Crime
prediction has always remained a hot topic in data mining, because law enforcement
agencies used these predictions and takes different steps.
In the modern era, where researchers implemented many techniques to minimize or
identifies crime patterns and identification using analysis of historical crime data and
their trends. In result, crimes are minimized, but we can’t get rid of crimes. One of the
most famous crime attacked the world trade center on 11, 2001. Some popular crimes in
London are listed down according to their occurrence. Torso human floating in River
Thomas on 2001 [2]. Murder of Sally Anne Bowman who worked as a model and
hairdresser was raped in 2015 [3]. Ben Kinsella was an English student, he's murdered
by a gang of black teenagers in 29, June 2008 [4]. Tia Sharp was a high-profile case of
child murder her dead body found in her grandfather in August 2012 [5]. Gemma
Mccluskie who worked as an actress, her body discovered in the Regent Canal on
March 2012 [6]. Lee Rigby walked on Wellington Street, two men killed him with
knives on May 2013 [7]. Alice was a 14-year-old girl, missing August 2014 and found
her body in Boston Manor Park on 28 August 2014 [8]. Many crimes became the
headline of television. Law enforcement agencies, researchers, and computer analysts
are working together for many years to minimize crime rate.
We proposed an approach to the forecasting crime rate in a different borough of London
and forecast crime pattern graph using historical data about crimes and gives crime
trend for future years. Our nature of a problem is to predict crime rate in London for
future by the availability of the dataset. The purpose of this research study is to
highlight those boroughs of London, where crime rate will be increase according to time
frame. This research is helpful to law enforcement agencies to work out in limited
resources. As no previous work done using ARIMA model to forecast crime rate.

2 Methods
Our section is divided into three subsections: Sect 3.1, 3.2 and 3.3. Section 3.1 describes
London crime (LC) dataset for choosing reasons. Section 3.2 describes the LC selection
because LC data set contains data of all boroughs of London with appropriate resources.
Section 3 describes data mining technique which we are applying for crime forecasting.

2.1 LC Dataset
Dataset gathering is challenging part of crime analyses and prediction. Crime dataset is
taken from thirty-four borough of London. The reason of the selection of borough of
London, because London police maintain rich data of crime on a daily basis and
distributed in monthly wise. Most of the verified data collected from their verified
sources. All the crimes are distributed in month wise of each city.
 Forecasting of future crime using Data Mining technique 3

2.2 LC selection of London dataset

The LC dataset approaches to choose four boroughs of London (Barking and Dagenham,
Barnet, Bexley and Brent) based upon crime rates in this borough. A total number of
crimes from 2012 to 2016 are analyzed using graph (please refer Fig 1) shows the
borough wise distribution of crime in each borough. In line graph y axis shows a total
number of crimes in each city and x-axis show year wise distribution.

Fig 1. Number of crimes versus year for four London boroughs

2.3 Forecasting Technique

We start from LC dataset using two ways (1) collected crime records in unstructured
form from a web source, namely – Data police UK [7]. Data available from web sources
during the period 2012 – 2016. (2) Applying data processing techniques to clean
unstructured crime data and extracted into structured data with 2100 crime instances
(.csv format). The structured crime data represented borough and monthly crime rate
attributes. The structured data is implemented using two tools. (1) Microsoft Excel (2)
IBM SPSS. Microsoft Excel for data cleaning and processing. IBM SPSS for crime
prediction. Figure 2 shows LC dataset.

Fig 2. Structured data of London crime data set taken from the UK police website [47]
 Forecasting of future crime using Data Mining technique 4

3 Experiments
3.1 LC Dataset Approach
In this section, we discussed the flow of the proposed LC dataset using Fig 3. The LC
data set consists of (.csv) format. LC dataset is fully integrated with various techniques of
data mining, including data cleaning, integration, and reduction. IT gains us more
flexibility to detect crime patterns and predicted values. LC dataset will help law
enforcement agencies to predict crime of different borough and its rate. The proposed
work flow starts from LC dataset. We find and search London crime data from different
websites and other sources, then we follow data cleaning process to clear data and
remove raw data (Missing value). The LC dataset supplied with IBM SPSS software to
critical analyses of crime data, we perform some experiment through different model
included regression. Linear regression and ARIMA model. Finalized Model is an
ARIMA model because the performance of ARIMA model is more accurate and
forecasting values are comparatively similar to crime happened. On the basis of
prediction, law enforcement agencies manage police, according to the crime rate in each
city.

Fig 3. London Crime prediction work flow

3.2 Model & Algorithm Selection

Different algorithms are designed to analyze and identify a pattern of data in which
machine learning algorithms are used to predict values like linear regression, Decision
tree, Support vector machine, Random Forest etc. Many data science algorithms are
 Forecasting of future crime using Data Mining technique 5
used in determining the data pattern like visualization, text mining, and auto regression
moving the average model. The ARIMA model is selected to conduct an analysis of our
dataset.

Forecasting economic, industry, financial, marketing, population purposes ARIMA

model is a suitable selection across different models. Auto regression integrated moving
average (ARIMA) is successfully used for prediction. This model was created in 1970
by Gwilym, M.Jenkins and George E.P Box.

The forecasting ARIMA model of stationary time series of our crime dataset is

The predicted value of the crime data set is the = Constant / Sum of one or more recent
values of Y and recent values of error of Y

In crime model, Stationaries series called auto regression, forecasting of errors called
moving average and the series, which is different to be made stationary called
integrated. ARIMA model is constructed with (p, d, q) where p is auto regression, d is
the nonseasonal difference, q is logged forecast error. The forecasting equation of crime
data is constructed Y, denoted with a depth difference of Y.

If d = 0

Yt = Yt

If d = 1

Yt = Yt-Yt-1

If d = 2

Yt = (Yt-Yt-1) – (Yt-1-Yt-2)

The forecasting equation is

Ŷt = μ + ϕ1 yt-1 +…+ ϕp yt-p - θ1et-1 -…- θqet-q

Where moving average is defined by (θ’s) in terms of positive and negative sign. For
crime dataset, we first estimate different values in auto regression model. The best fit
value of crime data is

ARIMA (2, 0, 0)

The forecasting equation is

Ŷt = μ + ϕ1Yt-1

Now, we find series Y, crime data is not stationary, so predicted values are

ARIMA (0, 2, 0)

The general forecasting equation is

Ŷt - Yt-2 = μ

Ŷt = μ + Yt-2
 Forecasting of future crime using Data Mining technique 6
Both values are correlated with each other. We can add a dependent variable for
forecasting

Ŷt - Yt-2 = μ + ϕ1(Yt-1 - Yt-2)

Ŷt - Yt-1 = μ

The generalized equation of forecasting is

Ŷt = μ + Yt-1 + ϕ1 (Yt-1 - Yt-2)

The both values provide confidence level 1 which means that the interval will be
accepted.

LC dataset detects crime patterns and relation between crime data using ARIMA model
techniques. These techniques provide us to identify crime and facility in handling crime
information in each city. This data set is used for crime prevention. Crime based on each
city helps law enforcement agencies and government to take proper measure of police
against a criminal. For example, Camden has the highest rate of crime report among
seven boroughs of London. So law enforcement agencies should arrange special place
or increase police for this city.
 Forecasting of future crime using Data Mining technique 7

4 Results
In this section, we provide implementation details for the proposed approach
which gives a better result for long term crime forecasting. The outcomes,
values and graph of models are shown in Fig 4, 5, 6 and 7. As in our pictures, it
is found that the model fits with its series and predict better values which are
also useful in a real scenario. The overall accuracy of the ARIMA algorithm is
best for crime prediction. The algorithm gives the best value of R-squared
among lowest error value. To verify the model, we take from 2012 to 2015 and
predict 2016, the actual and predicted value is very close to reality. Because of
the accurate forecasting of data, we predicted crime rates for 2017 to 2018.

Fig 4. Forecasting Model of Brent Borough in London

Fig 5. Forecasting Model of Barking Borough in London

This result is beneficial and important for crime suppression for the local
government and police stations. Because of the accurate predictions of crimes
of the ARIMA model. We will take some future emergency measurements,
such as criminal activities, patrolling will be patrolling will be prepared in
advance and limited resources will be deployed rightly to minimize the crime
rate decision making will be improved greatly for the local police station and
municipal governments.
 Forecasting of future crime using Data Mining technique 8

Fig 6. Forecasting Model of Bexley Borough in London

Fig 6. Forecasting Model of Barnet Borough in London

5 Conclusions
Crime in London borough is continuously going on, which is dependent upon some
factors such as poverty, unemployment, frustration, etc. Police investigation agencies
take an active role against criminal but it takes much more time. So we contribute
towards for forecasting crime rate in a different borough of London. Our proposed
model extracts unstructured data from web sources including London police website.
Investigating agencies should use our proposed model to check the crime rate in the
future. This model helps and speeds up a process where crime rate will become higher.
We used time series ARIMA model is used to calculate crime rate for 2 years (2017 to
2018) by providing five years past data (2012 to 2016). This study presented the best fit
model for crime rates in London. The comparison between past crime rate and forecast
crime rate behaved well and this statistical record is also used in real scenarios. The
table 2 presents the forecasting values of 2017 and 2018. For predicting purpose, we
take values of present year 2017 for matching predicted values and actual values which
is 80% correct. Table 2 shows number of crime according to month. The upper
confidence limit (UCL) shows higher chances of crime. The lower confidence limit
shows lowest chances of crime. The forecast value is predicated value of crime based on
data.
 Forecasting of future crime using Data Mining technique 9

TABLE 1: MODEL STATISTICS

Number Model Fit statistics Ljung-Box Q(18) Number
Model of Stationary Statist of
Predictors R-squared R-squared DF Sig. Outliers
ics
Barking
Dagenham 0 .676 .588 26.405 16 .049 0
Model
Barnet-
0 .636 .636 16.278 16 .434 0
Model
Bexley-
0 .743 .535 38.989 16 .001 0
Model
Brent-
0 .614 .690 4.971 16 .996 0
Model

TABLE 2: MODEL STATISTICS

Model Barnet-Model Barking Dagenham- Bexley-Model Brent-Model_1
Model
Forecast UCL LCL Forecast UCL LCL Forecast UCL LCL Forecast UCL LCL
Jan-17 2048 2231 1866 1437 1574 1300 1139 1260 1019 2363 2567 2159
Feb- 1967 2164 1770 1366 1513 1219 1037 1160 913 2191 2430 1953
17
Mar- 2184 2394 1973 1559 1716 1402 1169 1294 1043 2373 2641 2105
17
Apr- 2036 2258 1813 1355 1522 1189 1064 1192 936 2204 2498 1909
17
May- 2091 2325 1857 1475 1650 1300 1139 1269 1008 2416 2736 2097
17
Jun-17 2077 2323 1832 1412 1596 1228 1122 1254 989 2358 2700 2016
Jul-17 2144 2400 1888 1520 1711 1328 1172 1306 1037 2358 2721 1995
Aug- 1999 2265 1732 1374 1573 1174 1044 1181 908 2285 2669 1902
17
Sep- 2010 2286 1734 1384 1590 1177 1095 1234 956 2230 2633 1828
17
Oct- 2193 2479 1907 1402 1616 1188 1201 1342 1060 2440 2861 2020
17
Nov- 2217 2512 1922 1473 1694 1252 1183 1326 1040 2422 2860 1984
17
Dec- 2089 2393 1785 1346 1573 1119 1182 1327 1036 2277 2732 1822
17
Jan-18 2048 2361 1736 1437 1671 1203 1139 1287 992 2363 2834 1892
Feb- 1967 2288 1646 1366 1606 1126 1037 1186 887 2191 2678 1704
18
Mar- 2184 2513 1854 1559 1805 1313 1169 1320 1018 2373 2875 1871
18
Apr- 2036 2373 1698 1355 1608 1103 1064 1217 911 2204 2721 1687
18
May- 2091 2436 1746 1475 1733 1217 1139 1293 984 2416 2948 1885
18
Jun-18 2077 2430 1725 1412 1676 1148 1122 1278 965 2358 2903 1813
Jul-18 2144 2504 1784 1520 1789 1250 1172 1330 1013 2358 2917 1799
Aug- 1999 2366 1631 1374 1649 1099 1044 1205 884 2285 2857 1713
18
Sep- 2010 2385 1635 1384 1664 1103 1095 1257 933 2230 2816 1645
18
Oct- 2193 2575 1811 1402 1688 1116 1201 1365 1037 2440 3038 1842
18
Nov- 2217 2606 1828 1473 1764 1182 1183 1349 1018 2422 3032 1812
18
Dec- 2089 2485 1693 1346 1642 1050 1182 1349 1014 2277 2900 1655
18
 Forecasting of future crime using Data Mining technique 10

6 Discussion
Literature survey includes many approaches on crime prediction with some limitation.
Different authors discussed different approaches for crime prediction. Most of the
common discussion is crime classification using different clustering algorithms.
Aghababaei et al. [9] discussed crime prediction based on posted tweets, however, they
don’t provide training dataset to evaluate results and measure performance accurately.
Although some authors S.R Deskmukh et al. 2015; Akshay Kumar Singh et al. 2016;
A.Bharathi et al. 2014; Tushar Sonaqwanev et al. 2015; [10]-[11]-[12]-[13] discussed
crime prediction using data mining techniques, apply different algorithms K-Mean,
Apriori algorithms, naive Bayes classifiers. Thongtae and Sirsuk 2008; [14] Shiju
Sathyadeven et al. 2014; [15] Lawrence and Natarajan 2015 [16]; Malathi et al. 2011;
[17] discussed crime classification, patterns based on the training dataset. Training data
set used as knowledge discovery for future predictions. Although some work is done in
crime detection Shyam Varan Wath 2006; [18] Chung Hisen et al. 2011; [19] Vineet et
al. 2016 [20] discussed semi-supervised learning, support vector machine (SVM), a
decision tree for crime detection. Tahani et al. 2015; [21] discussed crime prediction
based upon the spatial and temporal dataset, compare two data sets and identify crime
types. S.Sivaranjani et al 2016; [22] work with crime activates using density based
spatial clustering and different algorithms. Pen Chang et al 2008; [23] discussed an
ARIMA model for forecasting crimes. Zakaria Suliman and Ayman Altaher 2013; [24]
Anisha Agarwal et al. 2016; [25] Anshu and Raman Kumar et al. 2013; [26] proposed a
model through crime data, analyze and suggest predicted the desired pattern. Lenin
Mookiah et al. 2015; [27] conducted crime survey in which they collected different
crime variables and rate. Tirthraj and Rajanikanth 2016; [28] Sushant Bharti and
Ashutosh 2015; [29] developed a predictive model for crime analytics, which helps law
enforcement authorities to allocate resources to higher areas where crime chances are
maximized. Although Abdul Awar et al. 2016; [30] discussed same work, but using
linear regression to predict future crime. Some work discussed on crime classification
Addarsh, Abhilash, and Poorna; [31]. Umair Saeed et al. 2015; [32] have analyzed
crime patterns by applying machine learning algorithms. Using an available dataset on
internet web based work also discussed Xinyn Chen et al 2015; [33] discussed crime
prediction using a twitter dataset to predict crime and location. Mark B. Mithchell et al
2007; [34] introduced web based crime toolkit to analyze crime. They developed a tool
for forecasting crime in Richmond city. Suzilah and Nurulhuda 2013; [35] identify
crimes based on forecasting technique. Adjusted decomposition techniques are used to
detect crimes. The research was taken out of Kedah city located in Malaysia.
Concluding remarks show that crime index is higher in the future, which directly effect
on the economy of Malaysia. Gabriel Rosser et al. 2016; [36] discussed network based
crime mapping, a calibrated based model outperformed than grid alternative. 20%
crimes are more identified through this model. Aziz Nasiridinov et al. 2014; [37] detect
crime patterns using historical dataset. Four steps are followed to predict crimes. 1)
Algorithm selection 2) Generation steps 3) Result 4) Performance accuracy. The
proposed system is given to law enforcement agencies to detect or identify crimes. Tong
Wang et al. 2017; [38] Discussed and analyze different learning patterns for crimes. A
robustness are automatically detected crime pattern on a large dataset to save time-
consuming process. The purpose of the crime pattern detection algorithm known as
 Forecasting of future crime using Data Mining technique 11
Series Finder. Andrey Bogomolvo et al. 2014; [39] presented novel research on crime
based mobile data. Analyze human behavior from mobile to make crime prediction data
of human with basic geographic information. They obtain 70% accurate result of
predicted crimes. Bruno Cavadas et al. 2015; [40] proposed linear regression technique
applied to violet crime dataset. Learning system gives the best performance on
prediction. This system is limited to the USA. Vikas Grover et al. 2006; [41] examined
different techniques of crime prediction, including statistical method, offending
behavior, and geographical information. Many researchers spent a lot of time on data
analyzing. Limited techniques are available. Anchal Rani and Rajasree 2014; [42]
analysis of crime trends, Mahanolobis, Euclidean and Minkowski distance model and
time warping technique are used in multivariate time series to identify crimes. Wilpen et
al. 2013; [43] forecasting crime by selection of one month ahead and apply univariate
time series with the naïve method. The predicted values are more accurate than police
practices. Michael Hanslamaier et al. 2015 [44] forecasting crime in Germany, model
forecasting values till 2020. Based on their research offenses are expected to increase in
future. Hanmant et al. [45] Forecasting short term crime rate in Satara district. Secular
trend analysis is used to forecast crime value in short time. Saoumya and Baghel 2015;
[46] proposed a predictive model using big data. Crime mapping algorithm identifies
that area which is highly affected. Valuable data used in Artificial Neural Network for
future research on crime trend.

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