A Numerical Assessment of Some Recurrent Crime Series in the State of Pittsburg ^†

Abstract

The city of Pittsburg, Pennsylvania, remains -the epicenter of aggravated assaults this year. Compared to its pre-pandemic figures, violent crimes saw an upsurge with theft topping the city crime list. This study assessed the trend of crime series, particularly thefts, robberies, and burglaries, in two specific periods, namely from January 1990 to December 2001 and from 1 July 2023 to 30 September 2023, in Pittsburg using the discrete valued time series processes, with some popular innovation distributions that have recently emerged. The upward trend in thefts, robberies, and burglaries was affiliated with a shortage of police, existing police officers’ low morale, the latter’s anti-police demeanours, weak crime laws, gun proliferation, falling inflation rates, a rise in the consumers’ price index, uncomfortable homes, life insecurity, poverty, alcohol, drugs, and a devalued society. Thus, the implications include a need to strengthen existing crime laws, to create a diversion judiciary system offering alternatives to high-cost incarcerations provided that culprits adhere to the programs, and to establish evidence-based policies rooted in effective approaches.

1. Introduction

Although there was a decreasing trend in homicides in 2023, an exhaustive investigation of acerbated crimes in Pittsburg, Pennsylvania, shows that rates still appear to be elevated, with the attenuated lines up until this point showcasing an uptick compared to pre-pandemic figures. Theft and aggravated assaults were the predominant crimes committed, followed by arrest, vandalism, burglary, shooting, robbery, and arson from August 2023 to October 2023. In that same time frame, a total of 6323 crimes were registered by the Council of Criminal Justice Study [1]. In agreement with Braga, Hurcau and Papachristos [2] and Braga, Weisburd and Boxerman [3] and Sherman, and Gartin and Buerger [4], the above figures classify Pittsburg as a high-crime neighbourhood wherein a disproportionate number of violent crimes can occur within a fraction of time. In 2023, in August, 2408 crimes were registered, though these rates appeared to dwindle by 14 in September, with a further decrease of 873 in October. In total, 536 thefts, 48 robberies, 66 burglaries, 203 cases of vandalism, 55 shootings, and 553 arrests were recorded for August 2023. On the other hand, in September 2023, a slight decrease in crime was observed, with 547 assaults, 504 thefts, 41 robberies, 77 burglaries, 185 cases of vandalism, 52 shootings, 1 arson, and 500 arrests. Cold crimes, including the use of deadly weapons and the infliction of alarming bodily wounds on victims, were reported to rise by 8 percent from August to October 2023, which is above the figures registered in the pre-pandemic period. Likewise, motor vehicle thefts that began during the COVID-19 pandemic amounted to 23,974 purloined vehicles being stolen from January to June 2023 [1]. According to the latest data from the police, the year 2022 saw 71 homicides, which was the highest total in the decennary, and 60 percent of the offenders and victims were within the age group of 15–24 years old. The study by Meyer, Hassafy, Lewis, Shrestha, Haviland and Nagin [5] hypothesized social chaos, economic unrest, and altered police demeanour as the underlying causes. However, according to Rosenfeld, a police officer who participated in the Council of Criminal Justice Study [1], there was a spike in the rate of homicides after the viral video of George Floyd’s death in police custody was posted. To him, Pennsylvanians, due to their mistrust in police officers and their propensity for racial prejudice, are likely to apply laws according their own interpretation. Understanding the increas in crimes in Pittsburg entails reimagining policing in the city, alongside empirical elucidations for the data on crimes.

In this paper, we focus on the series of thefts, robberies and burglaries that occurred in the state of Pittsburg during two specific time periods for comparative purposes. The first period covers January 90 to December 2001 and the second period is from July 2023 to September 2023. The analysis of these two series is conducted using the discrete-valued time series processes, which is explained in the next section. The paper is thus organized as follows: The next section deals with the time series structures and distributional properties. This is followed by some Monte Carlo simulation studies and their application to the Pittsburg crime series. The paper ends with a section containing our conclusions.

2. Materials and Methods

2.1. The INAR(1) Process with the Poisson–Bilal (INAR(1)PB Innovation

McKenzie [6,7] introduced the first-order integer-valued auto-regressive process (INAR(1)), which is based on the Steutel and Van Harn [8] binomial thinning operator, where the random count observation at the $t^{th}$ time point, $Y_t$, is allowed to depend on the previous $Y_{t-1}$, via an auto-regressive equation of the following form:

$$Y_t=\left\{\begin{array}{cc}{\rho }_t\circ Y_{t-1}+R_t,\hfill & w.p{\rho }_t;\hfill \\ R_t,\hfill & w.p(1-{\rho }_t),\hfill \end{array}\right.$$

(1)

where ${\rho }_t\in [0,1)$ is the survival probability. In this stochastic equation, $R_t$ is the random error term at the current $t^{th}$ time point, which is independent of the previous lagged observation, $Y_{t-1}$. The realization $y_t$ indicates a type of crime in the Pittsburg state at time t. ${\rho }_t$ can either be a constant or randomly distributed variable in the interval (0, 1); it can also be time-dependent in the form ${\rho }_t={\displaystyle \frac{\exp \left(x_t\mathit{\beta }\right)}{1+\exp \left(x_t\mathit{\beta }\right)}}$, where ${\mathbf{x}}_{\mathbf{t}}=\{x_{t,1},x_{t,2},\dots ,x_{t,p}\}$, and ${\rho }_t={\displaystyle \frac{\exp \left(x_t\mathit{\beta }\right)}{1+\exp \left(x_t\mathit{\beta }\right)}}$, where $\mathit{\beta }={\{{\beta }_1,{\beta }_2,\dots ,{\beta }_p\}}^T$ is the vector of regression coefficients (refer to papers by McKenzie [6,7], Jowaheer and Sutradhar [9], Chang et al. [10], Zhang and Wang [11], Sunecher and Mamode Khan [12,13] and Zhang et al. [14,15]). The model (1) has some elegant properties, which are as follows [16]:

(a)

$E({\rho }_t\circ Y_{t-1})=E\left({\rho }_t\right)E\left(Y_{t-1}\right)$

(b)

Var$({\rho }_t\circ Y_{t-1})=E{\left({\rho }_t\right)}^{2}Var\left(Y_{t-1}\right)+E\left({\rho }_t\right)[1-E\left({\rho }_t\right)]E\left(Y_{t-1}\right)+Var\left({\rho }_t\right)E[Y_{t-1}$$(Y_{t-1}-1)]$.

(c)

Cov$({\rho }_t\circ Y_{t-1},Y_{t-1})=E\left({\rho }_t\right)Var\left(Y_{t-1}\right)$.

(d)

Cov$(Y_t,Y_{t+h})={\sum }_{i=0}^{h-1}E\left({\rho }_{t+h-i}\right)Var\left(Y_t\right)$

Under the condition of constant ${\rho }_t$, these properties can be adjusted flexibly.

This paper introduces the stochastic process $\left\{Y_t\right\}$ with the most recent distribution for the innovation term $R_t$, known as the Discrete Poisson–Bilal (DPB) distribution. Some of the main properties of the DPB distribution are as follows:

$$\begin{array}{cc}\hfill P_{DPB}(r,\lambda )& =P(R_t=r)\hfill \\ \hfill & ={\displaystyle \frac{6}{\lambda }}\left[{\left(1+{\displaystyle \frac{2}{\lambda }}\right)}^{-x-1}-{\left(1+{\displaystyle \frac{3}{\lambda }}\right)}^{-r-1}\right];r=0,1,2,3,\dots \hfill \end{array}$$

(2)

The moment-generating function (MGF) can be obtained as

$$M_{R_t}\left(t\right)={\displaystyle \frac{6}{(3+\lambda -\lambda e^t)(2+\lambda -\lambda e^t)}}$$

(3)

and the probability-generating function (PGF) of $R_t$ is given by

$${\phi }_{R_t}\left(S\right):=E\left[s^{R_t}\right]={\displaystyle \frac{6}{(3+\lambda -\lambda S)(2+\lambda -\lambda S)}}.$$

(4)

$${\mu }_{R_t}=E\left(R_t\right)={\displaystyle \frac{5\lambda }{6}}$$

(5)

$${\sigma }_{R_t}^2=Var\left(R_t\right)={\displaystyle \frac{\lambda (30+13\lambda )}{36}}$$

(6)

The coefficent of skewness (CS) and coefficient kurtosis (CK) of the DPB distribution are given by

$$CS={\displaystyle \frac{2\lambda (90+117\lambda +35{\lambda }^2)}{{\left[\lambda (30+13\lambda )\right]}^{3/2}}}$$

(7)

$$CK={\displaystyle \frac{9(120+664\lambda +540{\lambda }^2+121{\lambda }^3)}{\lambda {(30+13\lambda )}^2}}$$

(8)

The moments of the proposed model are as follows:

$$E\left(Y_t\right)={\displaystyle \frac{5\lambda }{6(1-{\mu }_{\rho })}}$$

(9)

$$Var\left(Y_t\right)={\displaystyle \frac{a}{1-{\mu }_{\rho }^2-{\sigma }_{\rho }^2}}$$

(10)

where $a={\displaystyle \frac{5\lambda ({\mu }_{\rho }-{\mu }_{\rho }^2-{\sigma }_{\rho }^2)}{6(1-{\mu }_{\rho })}}+{\displaystyle \frac{\lambda (30+13\lambda )}{36}}+{\displaystyle \frac{25{\lambda }^2{\sigma }_{\rho }^2}{36{(1-{\mu }_{\rho })}^2}}$.

$$Cov(Y_t,Y_{t+h})={\mu }_{\rho }^{h}Var\left(Y_t\right)$$

(11)

Under stationarity,

$$E\left(Y_t\right)={\displaystyle \frac{5\lambda }{6(1-\rho )}}$$

(12)

$$Var\left(Y_t\right)={\displaystyle \frac{a}{1-{\rho }^2}}$$

(13)

where $a={\displaystyle \frac{5\lambda (\rho -{\rho }^2)}{6(1-\rho )}}+{\displaystyle \frac{\lambda (30+13\lambda )}{36}}$

$$Cov(Y_t,Y_{t+h})={\rho }^{h}Var\left(Y_t\right)$$

(14)

2.2. Estimation of Parameters: CML

From Equation (1), the transition probability from realization l to k is given by

$$Pr(Y_t=k|Y_{t-1}=l,{\rho }_t=\rho )={\displaystyle \frac{6}{\lambda }}\sum _{i=0}^{min(k,l)}{\rho }^i{(1-\rho )}^{l-i}\left[{\left(1+{\displaystyle \frac{2}{\lambda }}\right)}^{-k-i-l}-{\left(1+{\displaystyle \frac{3}{\lambda }}\right)}^{-k-i-l}\right]$$

(15)

for $k,l\ge 0$.

Hence,

$$Pr(Y_t=k|Y_{t-1}=l)={\int }_0^1{\displaystyle \frac{6}{\lambda }}\sum _{i=0}^{min(k,l)}{\rho }_t^i{(1-{\rho }_t)}^{l-i}\left[{\left(1+{\displaystyle \frac{2}{\lambda }}\right)}^{-k-i-l}-{\left(1+{\displaystyle \frac{3}{\lambda }}\right)}^{-k-i-l}\right]\times f\left({\rho }_t\right)$$

(16)

The conditional log-likelihood function is hence

$$\ell (.)=log\left[{\Pi }_{t=2}^{n}Pr(Y_t=y_t|Y_{t-1}=y_{t-1})\right]=\sum _{t=2}^{n}log\left[Pr(Y_t=y_t|Y_{t-1}=y_{t-1})\right]$$

(17)

The optim function in R is used to obtain the parameter estimates. McCabe et al. [17] proved that the estimators from Equation (11) are asymptotically normal, with standard errors obtained from the inverse of the information matrix.

3. Numerical Illustrations

This section explores some Monte Carlo simulation experiments with the fixed auto-correlation parameter ${\rho }_t$ at $\rho =0.5,0.9$. INAR(1) with the PB innovation is generated with various $\lambda$ values starting at $\lambda =0.5,1,5,10$ under three sample sizes: $T=60,100,500$. The estimation of the model parameters is conducted using the CML approach in Section 2.2. The simulated mean estimates, based on 2000 simulated runs of $\widehat{\rho }$ and $\widehat{\lambda }$, are shown in

Table 1. Simulated mean estimates of the parameters with corresponding standard errors for the INAR(1)PB model for different combinations of parameters.

T	$\mathit{\lambda }$	$\mathit{\rho }$	$\widehat{\mathit{\lambda }}$	$\widehat{\mathit{\rho }}$
60	0.5	0.5	0.4817 (0.1542)	0.5259 (0.1016)
100			0.4911 (0.1277)	0.5080 (0.0792)
500			0.5088 (0.0630)	0.5019 (0.0244)
60		0.9	0.4829 (0.1490)	0.8799 (0.1140)
100			0.4902 (0.1115)	0.8896 (0.0870)
500			0.5060 (0.0462)	0.9057 (0.0356)
60	1	0.5	1.2789 (0.1615)	0.4812 (0.1001)
100			1.1111 (0.1305)	0.4867 (0.0859)
500			1.0301 (0.0754)	0.5036 (0.0305)
60		0.9	0.9844 (0.1481)	0.8806 (0.1216)
100			0.9910 (0.1038)	0.8966 (0.0856)
500			1.0155 (0.0707)	0.9011 (0.0337)
60	5	0.5	4.7587 (0.1733)	0.4828 (0.1146)
100			4.8072 (0.1507)	0.4808 (0.0864)
500			5.0051 (0.0968)	0.5066 (0.0461)
60		0.9	4.821 (0.1687)	0.8864 (0.1187)
100			4.902 (0.1287)	0.8929 (0.0810)
500			5.0171 (0.0790)	0.9070 (0.0319)
60	10	0.5	9.8812 (0.1813)	0.4804 (0.1236)
100			9.8911 (0.1545)	0.4936 (0.0980)
500			10.0048 (0.0923)	0.5073 (0.0306)
60		0.9	9.8608 (0.1813)	0.8808 (0.1132)
100			9.9371 (0.1479)	0.8958 (0.0861)
500			10.0145 (0.0742)	0.9091 (0.0487)

:

The simulation results show that the estimates of both $\rho$ and $\lambda$ are consistent and the standard errors decrease as the number of time points increases.

3.1. Data Application

3.1.1. Series of Offences from January 1990 to December 2001

The time series for theft, robbery and burglary (available at https://www.pittsburghpa.gov/Safety/Police/Police-Data-Portal/PBP-Annual-Reports, and accessed on 1 February 2024) consists of 144 observations for each type of offence.

Table 2. Descriptive statistics for the number of crimes from January 1990 to December 2001.

Crimes	Mean	Variance	Fisher Index
Theft	13.1035	121.0238	9.2360
Robbery	3.0175	10.7363	3.5580
Burglary	7.5795	37.6811	4.9714

below provides the means and variances for the different crimes. We propose fitting these series using INAR(1) with different innovations under fixed thinning. The series are both significantly auto-correlated, with a major quantum of over-dispersion. Hence, the modelling of such series can proceed with over-dispersed innovation distributions. In order to identify the most suitable INAR(1), we compare the AICs of several INAR(1), including INAR(1) with Negative Binomial (NB), INAR(1) with Conway–Maxwell–Poisson (CMP), INAR(1) with Poisson–Lindley (PL), INAR(1) with Poisson Inverse Gaussian (PIG), and then select the best model for further analysis and forecasting.

The qcc.overdispersion test in R testifies that the three series are significantly over-dispersed. The series are also tested while stationary and serially auto-correlated.

Table 3. Parameter estimates with sd in () for INAR(1)PB, INAR(1)PL and INAR(1)NB for the number of crimes from January 1990 to December 2001.

Offence	Parameter	Model
		PB	PL	NB
Theft	$\widehat{\rho }$	0.4802 (0.0041)	0.4993 (0.0040)	0.5291 (0.0040)
	$\widehat{\lambda }$	8.1353 (0.0894)	0.2728 (0.0029)	6.1702 (0.0886)
	$\widehat{\nu }$			1.0109 (0.0265)
	AIC	−39,024.88	−38,759.24	−38,477.28
Robbery	$\widehat{\rho }$	0.4037 (0.0063)	0.4161 (0.0063)	0.4329 (0.0064)
	$\widehat{\lambda }$	2.1538 (0.0310)	0.8743 (0.0119)	1.7118 (0.0312)
	$\widehat{\nu }$			1.2317 (0.0467)
	AIC	−25,507.28	−25,229	−25,090.96
Burglary	$\widehat{\rho }$	0.4185 (0.0049)	0.4434 (0.0049)	0.4583 (0.0048)
	$\widehat{\lambda }$	5.2776 (0.0619)	0.4060 (0.0046)	4.1072 (0.0572)
	$\widehat{\nu }$			0.8348 (0.0253)
	AIC	−33,646.42	−33,506.40	−33,456.78

and

Table 4. Parameter estimates with sd in () for INAR(1)PInvG and INAR(1)CMP for the number of crimes from January 1990 to December 2001.

Offence	Parameter	Model
		PInvG	CMP
Theft	$\widehat{\rho }$	0.5124 (0.0040)	0.6182 (0.0031)
	$\widehat{\lambda }$	6.3910 (0.0977)	0.6046 (0.0010)
	$\widehat{\nu }$	5.3194 (0.1792)	−0.1169 (0.0005)
	AIC	−38,690.90	−35,528.04
Robbery	$\widehat{\rho }$	0.4257 (0.0064)	0.6314 (0.0049)
	$\widehat{\lambda }$	1.7332 (0.0324)	0.1019 (0.0064)
	$\widehat{\nu }$	1.2277 (0.0600)	−0.1875 (0.0009)
	AIC	−25,153.60	−21,871.24
Burglary	$\widehat{\rho }$	0.4410 (0.0048)	0.6224 (0.0033)
	$\widehat{\lambda }$	4.2372 (0.0600)	0.4180 (0.0008)
	$\widehat{\nu }$	4.6524 (0.1758)	−0.2187 (0.0006)
	AIC	−33,532.68	−28,501

provide the model estimates under the different models.

The results clearly show that INAR(1)PB and INAR(1)PL yield better AICs than the other competitive models, with INAR(1)PB slightly providing better fitting criteria. Henceforth, using the PB and PL models and including the corresponding model estimates in Equation (1), we run simulations for 1000 horizons to obtain the sequence of predicted values. The median of this set of values is assumed to be the forecasted value. This process is then repeated iteratively for the next 10 forecasts using the updated values of $y_t$. The root mean square errors under INAR(1)PB and INAR(1)PL yield 0.9910 and 1.2112, respectively.

3.1.2. Crimes Series from 1 July 2023 to 30 September 2023

Three series on thefts, arrests and assaults were extracted from the Pittsburg website on 1 February 2024: https://www.pittsburghpa.gov/Safety/Police/Police-Data-Portal/PBP-Annual-Reports for the period starting July to end September. The mean (variance) of these series and their Fisher index of dispersion are shown in

Table 5. Descriptive statistics for the number of crimes from 1 July 2023 to 30 September 2023.

Crimes	Mean	Variance	Fisher Index
Theft	18.4348	47.4353	2.5731
Robbery	1.6839	2.1782	1.2935
Burglary	2.1087	2.8452	1.3493

below:

From the above results, INAR(1)PL and INAR(1) PB yield better AICs than the other competitive models, but INAR(1) PL gives a slightly better fit than INAR(1)PB. Overall, we may conclude that the newly proposed INAR(1)PB is a recommendable model. On the other hand, we implemented INAR(1) PB with Beta-distributed $\rho$, that is, $\rho \sim (\alpha ,1-\alpha )$, and the results of INAR(1)PB and INAR(1)PL are shown in

Table 6. Parameter estimates with sd in () for INAR(1)PB and INAR(1)PL for number of crimes from 1 July 2023 to 30 September 2023.

Offence	Parameter	Model
		PB	PL
Theft	$\widehat{\rho }$	0.3986 (0.0330)	0.4185 (0.0329)
	$\widehat{\lambda }$	13.2309 (1.1134)	0.1741 (0.0144)
	AIC	−619.8	−622.02
Robbery	$\widehat{\rho }$	0.0319 (0.0695)	0.0804 (0.0688)
	$\widehat{\lambda }$	1.9032 (0.2159)	0.9919 (0.1088)
	AIC	−304.05	−308.62
Burglary	$\widehat{\rho }$	0.2152 (0.0633)	0.2728 (0.0611)
	$\widehat{\lambda }$	2.0020 (0.2328)	0.9693 (0.1089)
	AIC	−326.06	−330.41

,

Table 7. Parameter estimates with sd in () for INAR(1)PInvG for the number of crimes from 1 July 2023 to 30 September 2023.

Offence	Parameter	Model
		PInvG	CMP
Theft	$\widehat{\rho }$	0.0785 (0.0339)	0.0729 (0.0354)
	$\widehat{\lambda }$	16.8983 (0.7230)	2.6720 (0.0423)
	$\widehat{\nu }$	163.0481 (42.8347)	0.3540 (0.0055)
	AIC	−600.2546	−598.48
Robbery	$\widehat{\rho }$	0.0041 (0.0610)	0.0058 (0.0625)
	$\widehat{\lambda }$	2.3705 (0.2501)	0.9461 (0.1129)
	$\widehat{\nu }$	13.6229 (49.6299)	0.1750 (0.0034)
	AIC	−290.12	−297.67
Burglary	$\widehat{\rho }$	0.0888 (0.0631)	0.0728 (0.0615)
	$\widehat{\lambda }$	1.9333 (0.1719)	0.8797 (0.1139)
	$\widehat{\nu }$	11.3773 (7.5373)	0.1546 (0.0024)
	AIC	−319.15	−315.42

and

Table 8. Parameter estimates with Beta-distributed $\rho$ with sd in () for INAR(1)PB and INAR(1)PL for number of crimes from 1 July 2023 to 30 September 2023.

Offence	Parameter	Model
		PB	PL
Theft	$\widehat{\alpha }$	0.6611 (0.0309)	0.7451 (0.0303)
	$\widehat{\lambda }$	14.8788 (1.1071)	0.1992 (0.0131)
	AIC	−624.3	−627.2
Robbery	$\widehat{\alpha }$	0.6922 (0.0612)	0.7433 (0.0635)
	$\widehat{\lambda }$	1.8781 (0.2043)	1.0023 (0.1056)
	AIC	−307.01	−313.02
Burglary	$\widehat{\alpha }$	0.7092 (0.0599)	0.7331 (0.0602)
	$\widehat{\lambda }$	2.1521 (0.2289)	0.9845 (0.1011)
	AIC	−331.24	−334.51

:

In comparison with Table 6, the standard errors of the estimates in the table above decreased with better AICs as well. Hence, the random coefficient INAR(1) models with PB and PL innovations are strongly recommendable.

4. Discussion

From the perspectives of crime analysts and police officers, a surge in crime, particularly theft, robbery, and burglary, in Pittsburg is due to the temporary decline in the public’s perceptions of law enforcement following widespread international uproar over Black Americans’ deaths in police custody. Alongside the Council of Criminal Justice [1], research conducted by news outlets, notably the CBC, underscored police staffing to be below budgeted levels, with fewer citizens showing interest in joining the police forces. Existing police officers, on the other hand, are reported to be worn out and in low morale due to the persistent public culture in response to the death of George Floyd. Anti-police behaviours and the proliferation of gums among Pennsylvanians have also caused the worsened tensions observed. In addition to this, the police have theorized that the increase in theft, robbery, and burglary comes ‘from pain’, including culprits being stuck in uncomfortable homes, life insecurity, poverty, alcohol and drug consumption and a devalued society. Following this logic, the above-mentioned crimes are a bid for liveable conditions and everyday security. Furthermore, the decreasing inflation rate and the rise in the consumer price index by 3 percent are underlined to have escalated theft, robbery, and burglary in 2023. In fact, comparing Table 2 with Table 5, we can notice some increase in the average number of thefts.

Noteworthy is that the above-stated reasons are speculations drawn by both Pittsburg’s police department and the Council of Criminal Justice [1]. Records of this kind lead to collaborative steps being taken by law enforcers, policymakers, and community-based organizations to establish evidence-based measures in Pittsburg to render it safe. Currently, crime justice reform efforts appear to be ineffective in lowering crime rates; contrarily, elected officials are endeavoring to improve the situation, particularly through implementing no-knock warrants, reducing solitary incarceration, establishing problem-solving courts, promoting pre-arrest diversion, introducing bail reforms, and reducing the number of detainees as driving catalysts for a prevention of crime. Ironically, instead of reducing crime rates and strengthening legal protocols, the efforts appear to have enabled criminals by weakening existing laws, ultimately failing the victims. Henceforth, the legal prosecution community should conduct extensive research on crime figures to endorse an enhanced plan of action, notably the setting up of a diversion judiciary system that provides alternatives to imprisonment as long as the subjects adhere to the legal pursuance programs. This would eventually help Pittsburg cut down the enormous amount of money allotted to incarceration. Besides the Crimes Trends Working Group launched by the Council of Criminal Justice in April 2023 to discuss crime rates and the reforms to be made, evidence-based policies grounded in effective practices should be pursued.

5. Conclusions

This study investigates the trend in thefts, robberies, and burglaries across two time spans, particularly from January 1990 to December 2001, and from July 2023 to September 2023, using the valued time series processes in Pittsburg, Pennsylvania. Our findings reveal a substantial increase in thefts, robberies, and burglaries in 2023, and according to the Pittsburg Police and the Council of Criminal Justice [1], this is due to the legal, economic, and social turbulences mentioned in the above section. An evaluation of the situation leads to recommendations to adopt holistic measures other than policing to reduce crime rates. Funding allocations from the Public Safety Budget to promote dialogue among Pennsylvanians, the Pittsburg Bureau of Police, municipalities of police, and social, mental and economic professionals about crime deterrence is recommended. Apart from yielding a comprehensive understanding of crimes, this endeavor may improve community relations as far as the criminalization of people of colour is concerned. Additionally, increased economic inclusion, notably job creation, living-wage policies, stronger minimum remuneration protocols, tax reduction, and the provision of free social services, can be considered to reduce socio-economic disparities in the Pittsburg area. Victims’ families, alongside those of the perpetrators, should receive mental and social services to ensure their smooth moral integration in the community, especially in cases wherein family members, notably children, are physically, emotionally, and mentally affected by the unanticipated crimes. Financial assistance to their children, distinctly for educational purposes, and guidance through community engagement activities, to foster their success, are also endorsed. In terms of a statistical model, INAR(1)PB seems to be a promising discrete-valued time series model with which to analyze crime series.