# Domestic Credit Growth Analysis using ARIMA Technique: A Case Study of Kenya

John K Njenga

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John K Njenga. Domestic Credit Growth Analysis using ARIMA Technique: A Case Study of Kenya. Journal of Economics, Management and Trade, 2024, 10.9734/JEMT/2024/v30i51206. hal-04542996

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# Domestic Credit Growth Analysis using ARIMA
## Technique: A Case Study of Kenya

John K Njenga

► To cite this version:

John K Njenga. Domestic Credit Growth Analysis using ARIMA Technique: A Case Study of Kenya. Journal of Economics, Management and Trade, 2024, 10.9734/JEMT/2024/v30i51206. hal-04542996

HAL Id: hal-04542996

https://hal.science/hal-04542996v1

Submitted on 11 Apr 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
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# Domestic Credit Growth Analysis using ARIMA Technique: A Case Study of Kenya

John K. Njenga a*

a University of Nairobi Kenya, P.O Box 13187 - 00200 Nairobi, Kenya.

**Author's contribution**

The sole author designed, analyzed, interpreted and prepared the manuscript.

**Article Information**

DOI: 10.9734/JEMT/2024/v30i51206

**Open Peer Review History:**

This journal follows the Advanced Open Peer Review policy. Identity of the Reviewers, Editor(s) and additional Reviewers, peer review comments, different versions of the manuscript, comments of the editors, etc are available here: https://www.sdiarticle5.com/review-history/115407

Received: 03/02/2024

Accepted: 05/04/2024

Published: 11/04/2024

**Original Research Article**

## ABSTRACT

The aim of this paper is to technically analyze domestic credit growth in Kenya using the Box-Jenkin framework. Box-Jenkin technique uses ARIMA model, which is used to understand time series data and forecast future values of the observed data for a given period. The framework involves three iterative step to develop a model. The first step involves model parameter identification. Unit root test show that domestic credit is stationary after the first difference. The ACF and PACF indicates cut off at lag zero in both cases. There are seasonal component in the ARIMA model. In the second step of model estimation, ARIMA(2,1,2)(1,0,0)₁₂ is obtained as the best fit for the sample period under consideration. Model diagnostics test in the third step, proves that there ARIMA modeling assumptions are met. The estimated model is used to forecast credit growth for the next twelve monthly values in year 2024 upto December. The estimated model projects an increase trend in domestic credit growth for the year 2024, with the percentage growth rate ranging between 1.045 to 1.230 percent. The expected domestic credit value in December 2024 is yellow is highly likely to hit Kenya shilling 8.039 Trillions mark. Kenya government should put in place monetary policy that favors bank credit growth and competition in the banking sector.

<footnote>*Corresponding author: E-mail: jnonjenga@gmail.com;</footnote>
<figure><img src="image_2.png" /></figure>

# Domestic Credit Growth Analysis using ARIMA Technique: A Case Study of Kenya

John K. Njenga a*

a University of Nairobi Kenya, P.O Box 13187 - 00200 Nairobi, Kenya.

**Author's contribution**

The sole author designed, analyzed, interpreted and prepared the manuscript.

**Article Information**

DOI: 10.9734/JEMT/2024/v30i51206

**Open Peer Review History:**

This journal follows the Advanced Open Peer Review policy. Identity of the Reviewers, Editor(s) and additional Reviewers, peer review comments, different versions of the manuscript, comments of the editors, etc are available here: https://www.sdiarticle5.com/review-history/115407

Received: 03/02/2024

Accepted: 05/04/2024

Published: 11/04/2024

**Original Research Article**

## ABSTRACT

The aim of this paper is to technically analyze domestic credit growth in Kenya using the Box-Jenkin framework. Box-Jenkin technique uses ARIMA model, which is used to understand time series data and forecast future values of the observed data for a given period. The framework involves three iterative step to develop a model. The first step involves model parameter identification. Unit root test show that domestic credit is stationary after the first difference. The ACF and PACF indicates cut off at lag zero in both cases. There are seasonal component in the ARIMA model. In the second step of model estimation, ARIMA(2,1,2)(1,0,0)₁₂ is obtained as the best fit for the sample period under consideration. Model diagnostics test in the third step, proves that there ARIMA modeling assumptions are met. The estimated model is used to forecast credit growth for the next twelve monthly values in year 2024 upto December. The estimated model projects an increase trend in domestic credit growth for the year 2024, with the percentage growth rate ranging between 1.045 to 1.230 percent. The expected domestic credit value in December 2024 is yellow is highly likely to hit Kenya shilling 8.039 Trillions mark. Kenya government should put in place monetary policy that favors bank credit growth and competition in the banking sector.

<footnote>*Corresponding author: E-mail: jnonjenga@gmail.com;</footnote>
Keywords: ARIMA Model; Box-Jenkins Methodology; domestic credit; forecasting.

# 1 INTRODUCTION

Domestic credit in any economy, is an important macroeconomic variable. Its plays an important role in allocating resources for investment in an efficient way. Credit from banks awarded to enterprenuer agents is used for productive investment where the agent did not have own fund. Investment demands and composition increase with increase in credit availability (Khamis and Klossifov [1]). The overall impact is increase in employment and output level within an economy. In credit development, there is likelihood of either a boom or bust. This may be attributed to several factors both internal and external. A credit boom is most likely caused by a higher share of external bank bond lending as an external factor(Avdjiev et al. [2]). Factors in the financial sector such as financial sector privatization, liberalization of the current account, sector comprehensive reforms and increased banking sector competition are attributed to increase in credit growth within an economy (Aydin [3], Hansen and Sulla [4], Coudert and Pouvelle [5], and Hauner [6]).

Multivariate regression analysis of domestic credit and macroeconomic variables have been carried out, to determine key factors that contribute to domestic credit growth and the direction of the relationship. Domestic credit is positively affected by money supply growth, GDP growth, high degree of openness and increase in interest rates. On the other hand, macroeconomic variables such as gross capital formation and currency depreciation negatively affect domestic credit growth. (Islam [7], Sulaiman [8], Ndanshau and Semu [9]). The nexus between economic growth and domestic credit exhibit a significant positive relationship in Turkey and some Balkan countries (Alihodžić and Ekšić [10], Basha et al [11] and Wolde-Rufael [12]). There exists a significant causality between domestic credit and economic growth, with the direction of the causal link varying from one country to another (Gozgor [13], Stolbov [14] and Bui [15]). Another important macroeconomic interaction is that of international capital flows with domestic credit. Empirical research have proved that there exist a strong relationship between the two variables, with capital inflow having a positive effect on domestic credit growth (Lane and McQuade [16], Di Giovanni et al. [17] and Igan et al. [18]).

Uni-variate ARIMA approach and exponential smoothing has been used to model and forecast domestic credit. In Pakistan, Noreen et al. [19] observed that ARIMA (1,1,0) was a perfect fit for credit to private sector while ARIMA (3,2,3) fitted well in modelling credit to the public sector. Dinh [20] while analyzing and comparing China and Vietnam, observed that the best fit for Vietnam domestic credit was ARIMA (2,3,1) while in China it was ARIMA (2,3,5). Obeng-Amponsah [21] observed that exponential smoothing model with additive trend, multiplicative error and no seasonality was the optimal model to analyze and forecast Ghana domestic credit. In Kenya's context there have been research on credit impact on economic growth as a bivariate regression (Kiriga et al. [22]) and as a multivariate regression controlling for other factors considering the Comesa region (Kibet et al. [23]). The aim of this article is to determine an ARIMA model that best describes domestic credit and forecasting credit values for the next one year using the estimated model.

# 2 METHODOLOGY

## 2.1 Data

This study applied monthly banks domestic credit from January 2004 to December 2023. The data was obtained from Central Bank of Kenya (CBK) periodic statistical bulletins. A logarithm transformation is performed on the monthly domestic credit data to make the variance stable and reduce the effect outliers. From Fig. 1, there has been an increase in domestic credit over the sample period.

## 2.2 Model

### 2.2.1 Autoregressive (AR) Models

Consider a time series $y_t$ that has an autoregressive process of order p ie AR(p) expressed as;

$$y_t = \theta_1 y_{t-1} + \theta_2 y_{t-2} + \cdots + \theta_p y_{t-p} + \epsilon_t \quad (2.1)$$

For $t = 1, 2, \dots, T$ and $\epsilon_t \sim IID(0, \sigma^2)$ a white noise error process. In lag operator form, equation (2.1) reduces as follows

$$y_t - \theta_1 y_{t-1} - \theta_2 y_{t-2} - \cdots - \theta_p y_{t-p} = \epsilon_t \quad (2.2)$$
Keywords: ARIMA Model; Box-Jenkins Methodology; domestic credit; forecasting.

# 1 INTRODUCTION

Domestic credit in any economy, is an important macroeconomic variable. Its plays an important role in allocating resources for investment in an efficient way. Credit from banks awarded to enterprenuer agents is used for productive investment where the agent did not have own fund. Investment demands and composition increase with increase in credit availability (Khamis and Klossifov [1]). The overall impact is increase in employment and output level within an economy. In credit development, there is likelihood of either a boom or bust. This may be attributed to several factors both internal and external. A credit boom is most likely caused by a higher share of external bank bond lending as an external factor(Avdjiev et al. [2]). Factors in the financial sector such as financial sector privatization, liberalization of the current account, sector comprehensive reforms and increased banking sector competition are attributed to increase in credit growth within an economy (Aydin [3], Hansen and Sulla [4], Coudert and Pouvelle [5], and Hauner [6]).

Multivariate regression analysis of domestic credit and macroeconomic variables have been carried out, to determine key factors that contribute to domestic credit growth and the direction of the relationship. Domestic credit is positively affected by money supply growth, GDP growth, high degree of openness and increase in interest rates. On the other hand, macroeconomic variables such as gross capital formation and currency depreciation negatively affect domestic credit growth. (Islam [7], Sulaiman [8], Ndanshau and Semu [9]). The nexus between economic growth and domestic credit exhibit a significant positive relationship in Turkey and some Balkan countries (Alihodžić and Ekšić [10], Basha et al [11] and Wolde-Rufael [12]). There exists a significant causality between domestic credit and economic growth, with the direction of the causal link varying from one country to another (Gozgor [13], Stolbov [14] and Bui [15]). Another important macroeconomic interaction is that of international capital flows with domestic credit. Empirical research have proved that there exist a strong relationship between the two variables, with capital inflow having a positive effect on domestic credit growth (Lane and McQuade [16], Di Giovanni et al. [17] and Igan et al. [18]).

Uni-variate ARIMA approach and exponential smoothing has been used to model and forecast domestic credit. In Pakistan, Noreen et al. [19] observed that ARIMA (1,1,0) was a perfect fit for credit to private sector while ARIMA (3,2,3) fitted well in modelling credit to the public sector. Dinh [20] while analyzing and comparing China and Vietnam, observed that the best fit for Vietnam domestic credit was ARIMA (2,3,1) while in China it was ARIMA (2,3,5). Obeng-Amponsah [21] observed that exponential smoothing model with additive trend, multiplicative error and no seasonality was the optimal model to analyze and forecast Ghana domestic credit. In Kenya's context there have been research on credit impact on economic growth as a bivariate regression (Kiriga et al. [22]) and as a multivariate regression controlling for other factors considering the Comesa region (Kibet et al. [23]). The aim of this article is to determine an ARIMA model that best describes domestic credit and forecasting credit values for the next one year using the estimated model.

# 2 METHODOLOGY

## 2.1 Data

This study applied monthly banks domestic credit from January 2004 to December 2023. The data was obtained from Central Bank of Kenya (CBK) periodic statistical bulletins. A logarithm transformation is performed on the monthly domestic credit data to make the variance stable and reduce the effect outliers. From Fig. 1, there has been an increase in domestic credit over the sample period.

## 2.2 Model

### 2.2.1 Autoregressive (AR) Models

Consider a time series $y_t$ that has an autoregressive process of order p ie AR(p) expressed as;

$$y_t = \theta_1 y_{t-1} + \theta_2 y_{t-2} + \cdots + \theta_p y_{t-p} + \epsilon_t \quad (2.1)$$

For $t = 1, 2, \dots, T$ and $\epsilon_t \sim IID(0, \sigma^2)$ a white noise error process. In lag operator form, equation (2.1) reduces as follows

$$y_t - \theta_1 y_{t-1} - \theta_2 y_{t-2} - \cdots - \theta_p y_{t-p} = \epsilon_t \quad (2.2)$$
$$ \theta(L)y_t = \epsilon_t \quad (2.3) $$

for $\theta(L) = 1 - \theta_1 L - \theta_2 L^2 - \dots - \theta_p L^p$ is the characteristic polynomial for the AR(P) function.

## 2.2.2 Moving Average (MA) Models

For a time series $y_t$ that has a moving average process of order q ie MA(q) is expressed as series of white noise processes $\sim N(0, \sigma_e^2)$ as shown below

$$ y_t = \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.4) $$

The MA(q) is always stationary, as the observations are as a weighted moving average over past errors. In lag operator form, it's expressed as

$$ y_t = \phi(L) \epsilon_t \quad (2.5) $$

where the characteristic polynomial for the MA(q) is $\phi(L) = 1 + \phi_1 L + \phi_2 L^2 + \dots + \phi_q L^q$

## 2.2.3 Autoregressive Moving Average (ARMA) Models

An ARMA is a combined process of both autoregressive process of order p and series of white noise process of order q, forming ARMA (p,q) expressed as

$$ y_t = \theta_1 y_{t-1} + \theta_2 y_{t-2} + \dots + \theta_p y_{t-p} + \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.6) $$

Re-arranging equation (2.6)

$$ y_t - \theta_1 y_{t-1} - \theta_2 y_{t-2} - \dots - \theta_p y_{t-p} = \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.7) $$

In lag operator form, equation (2.7) is expressed as

$$ \theta(L)y_t = \phi(L) \epsilon_t \quad (2.8) $$

where $\theta(L)$ and $\phi(L)$ are the characteristic polynomial for the AR(P) and MA(q) respectively as indicated above.

### Kenya monthly domestic credit growth

<figure><img src="image_3.png" /><figcaption>Fig. 1. Monthly domestic credit plot</figcaption></figure>
$$ \theta(L)y_t = \epsilon_t \quad (2.3) $$

for $\theta(L) = 1 - \theta_1 L - \theta_2 L^2 - \dots - \theta_p L^p$ is the characteristic polynomial for the AR(P) function.

## 2.2.2 Moving Average (MA) Models

For a time series $y_t$ that has a moving average process of order q ie MA(q) is expressed as series of white noise processes $\sim N(0, \sigma_e^2)$ as shown below

$$ y_t = \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.4) $$

The MA(q) is always stationary, as the observations are as a weighted moving average over past errors. In lag operator form, it's expressed as

$$ y_t = \phi(L) \epsilon_t \quad (2.5) $$

where the characteristic polynomial for the MA(q) is $\phi(L) = 1 + \phi_1 L + \phi_2 L^2 + \dots + \phi_q L^q$

## 2.2.3 Autoregressive Moving Average (ARMA) Models

An ARMA is a combined process of both autoregressive process of order p and series of white noise process of order q, forming ARMA (p,q) expressed as

$$ y_t = \theta_1 y_{t-1} + \theta_2 y_{t-2} + \dots + \theta_p y_{t-p} + \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.6) $$

Re-arranging equation (2.6)

$$ y_t - \theta_1 y_{t-1} - \theta_2 y_{t-2} - \dots - \theta_p y_{t-p} = \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.7) $$

In lag operator form, equation (2.7) is expressed as

$$ \theta(L)y_t = \phi(L) \epsilon_t \quad (2.8) $$

where $\theta(L)$ and $\phi(L)$ are the characteristic polynomial for the AR(P) and MA(q) respectively as indicated above.

### Kenya monthly domestic credit growth

<figure><img src="image_3.png" /><figcaption>Fig. 1. Monthly domestic credit plot</figcaption></figure>
### 2.2.4 Autoregressive Integrated Moving Average (ARIMA) Models

Conversion of ARMA to ARIMA involves introduction of integration to ARMA process. The order of integration is the minimum number of differences required to obtain a stationary ARMA series. Since the moving average portion of the ARMA is always stationary, the autoregressive portion is always the cause for non-stationary. By making the autoregressive portion stationary by find the difference, equation (2.8) reduces to

$$ \theta(L)(1-L)^{d}y_{t} = \phi(L)\epsilon_{t} \quad (2.9) $$

where $(1-L)^d$ is the difference of order d. There are four special types of ARIMA

* ARIMA(0,0,0)- white noise process

* ARIMA (0,1,0)-Random walk process

* ARIMA(0,0,q)- Autoregressive process

* ARIMA(p,0,q)- autoregressive moving average

### 2.2.5 Seasonal Auto-Regressive Integrated Moving Average (SARIMA)

The ARIMA (p,d,q) in equation (2.9) is considered as non-seasonal ARIMA as it does not contain seasonal terms. Adding additional seasonal term to the non-seasonal ARIMA result to ARIMA(p,d,q)(P, D, Q)m. Where m is the number of observation per year and P,D,Q are seasonal period back shift of p,d,q respectively.

ARIMA(p,d,q)(P, D, Q)m is given as (Hyndman and Athanasopoulos, 2018)

$$ \theta(L)\Theta(L)(1-L)^{d}(1-L^{m})^{D}y_{t} = \phi(L)\Phi(L)\epsilon_{t} \quad (2.10) $$

For $\Theta(L) = 1 - \Theta_1 L^m - \Theta_2 L^{2m} - \dots - \Theta_{Pm} L^p$ and $\Phi(L) = 1 + \Phi_1 L^m + \Phi_2 L^{2m} + \dots + \Phi_Q L^{Qm}$

### 2.2.6 The Box – Jenkins Technique

Box and Jenkins [24] introduced an three steps which are iterative to model and forecast using ARIMA models

as follows;

* model identification

* Model estimation

* diagnostic checking steps (if the specification of a stationary univariate process fails, repeat the steps)

* forecast

#### (a) model identification

Model identification is the process of identifying the order of autoregressive process, integrated process and the moving average process corresponding to p,d,and q of ARIMA respectively.

To find a ARIMA model, it's a condition that the time series is stationary. A stationary times series is characterized by constant mean and variance. The mean and variance may be variant as a result of deterministic trend in a time series. To make a time series stationary, the integration process is performed, which is simply finding the difference of the time series. Within the model identification step, unit root test is performed to test for stationary and determine the integration order of a time series. This study applied ADF test (Dickey and Fuller, [25] and [26]) and P-P test (Phillips and Perron [27]). The model used in testing ADF test is as formulated in equation (2.11) while for P-P test is as defined in equation (2.12);

$$ y_t = c + \delta t + \phi y_{t-1} + \beta_1 \Delta y_{t-1} + \dots + \beta_p \Delta y_{t-p} + \epsilon_t \quad (2.11) $$

$$ y_t = c + \delta t + \phi y_{t-1} + \epsilon_t \quad (2.12) $$

Both unit root test use similar test statistic defined as;

$$ ADF_{\tau} = \frac{\hat{\phi} - 1}{SE(\hat{\phi})} \quad (2.13) $$

The null hypothesis for unit root tests states that there exist unit root ie $H_0: \phi = 1$ against an alternative hypothesis of $\phi < 1$.

<table><caption>Table 1. Unit root test result</caption><thead><tr><th rowspan="2"></th><th colspan="2">ADF test</th><th colspan="2">P-P Test</th></tr><tr><th>statistics</th><th>pvalue</th><th>statistics</th><th>pvalue</th></tr></thead><tbody><tr><td>In level</td><td>-0.8464</td><td>0.9564</td><td>-1.6564</td><td>0.9769</td></tr><tr><td>Δ<sup>1</sup></td><td>-4.8469</td><td>0.01</td><td>-250.49</td><td>0.01</td></tr></tbody></table>
### 2.2.4 Autoregressive Integrated Moving Average (ARIMA) Models

Conversion of ARMA to ARIMA involves introduction of integration to ARMA process. The order of integration is the minimum number of differences required to obtain a stationary ARMA series. Since the moving average portion of the ARMA is always stationary, the autoregressive portion is always the cause for non-stationary. By making the autoregressive portion stationary by find the difference, equation (2.8) reduces to

$$ \theta(L)(1-L)^{d}y_{t} = \phi(L)\epsilon_{t} \quad (2.9) $$

where $(1-L)^d$ is the difference of order d. There are four special types of ARIMA

* ARIMA(0,0,0)- white noise process

* ARIMA (0,1,0)-Random walk process

* ARIMA(0,0,q)- Autoregressive process

* ARIMA(p,0,q)- autoregressive moving average

### 2.2.5 Seasonal Auto-Regressive Integrated Moving Average (SARIMA)

The ARIMA (p,d,q) in equation (2.9) is considered as non-seasonal ARIMA as it does not contain seasonal terms. Adding additional seasonal term to the non-seasonal ARIMA result to ARIMA(p,d,q)(P, D, Q)m. Where m is the number of observation per year and P,D,Q are seasonal period back shift of p,d,q respectively.

ARIMA(p,d,q)(P, D, Q)m is given as (Hyndman and Athanasopoulos, 2018)

$$ \theta(L)\Theta(L)(1-L)^{d}(1-L^{m})^{D}y_{t} = \phi(L)\Phi(L)\epsilon_{t} \quad (2.10) $$

For $\Theta(L) = 1 - \Theta_1 L^m - \Theta_2 L^{2m} - \dots - \Theta_{Pm} L^p$ and $\Phi(L) = 1 + \Phi_1 L^m + \Phi_2 L^{2m} + \dots + \Phi_Q L^{Qm}$

### 2.2.6 The Box – Jenkins Technique

Box and Jenkins [24] introduced an three steps which are iterative to model and forecast using ARIMA models

as follows;

* model identification

* Model estimation

* diagnostic checking steps (if the specification of a stationary univariate process fails, repeat the steps)

* forecast

#### (a) model identification

Model identification is the process of identifying the order of autoregressive process, integrated process and the moving average process corresponding to p,d,and q of ARIMA respectively.

To find a ARIMA model, it's a condition that the time series is stationary. A stationary times series is characterized by constant mean and variance. The mean and variance may be variant as a result of deterministic trend in a time series. To make a time series stationary, the integration process is performed, which is simply finding the difference of the time series. Within the model identification step, unit root test is performed to test for stationary and determine the integration order of a time series. This study applied ADF test (Dickey and Fuller, [25] and [26]) and P-P test (Phillips and Perron [27]). The model used in testing ADF test is as formulated in equation (2.11) while for P-P test is as defined in equation (2.12);

$$ y_t = c + \delta t + \phi y_{t-1} + \beta_1 \Delta y_{t-1} + \dots + \beta_p \Delta y_{t-p} + \epsilon_t \quad (2.11) $$

$$ y_t = c + \delta t + \phi y_{t-1} + \epsilon_t \quad (2.12) $$

Both unit root test use similar test statistic defined as;

$$ ADF_{\tau} = \frac{\hat{\phi} - 1}{SE(\hat{\phi})} \quad (2.13) $$

The null hypothesis for unit root tests states that there exist unit root ie $H_0: \phi = 1$ against an alternative hypothesis of $\phi < 1$.

<table><caption>Table 1. Unit root test result</caption><thead><tr><th rowspan="2"></th><th colspan="2">ADF test</th><th colspan="2">P-P Test</th></tr><tr><th>statistics</th><th>pvalue</th><th>statistics</th><th>pvalue</th></tr></thead><tbody><tr><td>In level</td><td>-0.8464</td><td>0.9564</td><td>-1.6564</td><td>0.9769</td></tr><tr><td>Δ<sup>1</sup></td><td>-4.8469</td><td>0.01</td><td>-250.49</td><td>0.01</td></tr></tbody></table>
Both unit root test are in agreement that the decision is to fail to reject the null hypothesis in level as their p-values are greater than 0.05. In level, monthly domestic credit rate is non stationary. This indicates there exists a significant effect of external shocks on domestic credit. Over the sample period, domestic credit is heterogeneous and non constant mean. After the first difference, domestic credit attains stationary properties as the p-value is less than 0.05, thus reject the null hypothesis of non-stationary. Monthly domestic credit is of integrated of order 1 ie I(1) thus the value of d in ARIMA(p,d,q) is 1.

Box and Jenkins proposed autocorrelation function (ACF) and partial autocorrelation function (PACF) to generate empirical autocorrelations pattern. The formula for ACF ($\rho_h$) and PACF ($\phi_{h,h}$) are given as in equation (2.14) and (2.15) respectively.

$$ \rho_h = corr(y_t, y_{t-h}) = \frac{\gamma_h}{\gamma_0} \qquad (2.14) $$

$$ \phi_{h,h} = cov(y_t, y_{t+h} | y_{t+1}, y_{t+2}, \dots, y_{t+h-1}) \quad (2.15) $$

Where $h = 1, 2, 3, \dots, n-1$, $\gamma_h = cov(y_t, y_{t-h})$ and $\gamma_0$ is the covariance at lag zero. The behavior of ACF for AR(p) is gradual tail off while for MA(q) it cut off at lag q. On the other hand, PACF for AR(P) cuts off at lags q while for MA(q) there is a gradual tail off.

From Fig. 2 (a), ACF tips off at lag 0 and there is a significant spike at lag 4. Similarly, PACF tips off at lag 0 with significant spike at lag 9 as shown in Fig. 2 (b). This is an indication of a seasonal component in domestic credit. The optimal model considering the ACF and PACF is ARIMA(0,1,0)(1,0,0)$_{12}$.

## (b) Model estimation

Model estimation involves estimating the model parameter corresponding to the moving average process, the autoregressive process and the seasonal process, with the information score for the model included. The parameters are estimated maximizing the function (Hyndman and Athanasopoulos [28]);

$$ L^*(Y_t|Y_{t-1}, \delta_0) \qquad (2.16) $$

where $L^*$ is the conditional likelihood function without the constant terms and $\delta_0 = (\phi, \theta)$

Information criterion is a technique for selecting a model from a finite set of model. Akaike's information criterion (AIC), corrected Akaike's information criterion ($AIC_c$) and Bayesian information criterion (BIC) are considered

in this study. The better model fit is the one that has lower values of AIC and BIC. For any given model, the AIC is given as

$$ AIC = -2\log L(\hat{\theta}) + 2k \qquad (2.17) $$

where $\log L(\hat{\theta})$ is the maximized log-likelihood function with k parameter and t sample data points. Corrected AIC is given as;

$$ AIC_c = AIC + \frac{2k(k+1)}{n-k-1} \qquad (2.18) $$

Similarly, for any model the BIC is given as

$$ BIC = -2\log L(\hat{\theta}) + k\log(t) \qquad (2.19) $$

Three measure of accuracy are considered, namely; namely mean absolute error (MAE), root mean square error (RMSE) and mean average absolute error (MAPE) formulated as shown in equations (2.20), (2.21) and (2.22) respectively.

$$ MAE = \frac{1}{n} \sum_{i=1}^{n} |e_i| \qquad (2.20) $$

$$ RMSE = \sqrt{\frac{\sum_{i=1}^{n} e_i^2}{n}} \qquad (2.21) $$

$$ MAPE = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{e_i}{y_i} \right| \qquad (2.22) $$

The auto.arima function in forecast package in R software, which returns the best ARIMA model according to AIC, $AIC_c$ and BIC values based on step-wise algorithm, is used to return the best model. To model domestic credit, ARIMA(2,1,2)(1,0,0)$_{12}$ is the best fit. The parameter estimates are as shown in table 2. The estimated model has a white noise of 0.0132 standard deviation and a log-likelihood statistic of 697.43. From the measure of accuracy result, on average the fitted model is less than one percent off the observed values.

## (c) diagnostic test

ARIMA model residual analysis involves autocorrelation, heteroscedasticity and normality tests. Normality test uses Ljung-Box test statistics given as

$$ Q(m) = n(n+2) \sum_{k=1}^{m} \frac{r_k^2}{n-k} \qquad (2.23) $$

where n is the sample size, $r_k^2$ is autocorrelation of sample at k lags and m is the lag order. Autocorrelation test is performed by residual ACF test while heteroscedasticity test is performed by
Both unit root test are in agreement that the decision is to fail to reject the null hypothesis in level as their p-values are greater than 0.05. In level, monthly domestic credit rate is non stationary. This indicates there exists a significant effect of external shocks on domestic credit. Over the sample period, domestic credit is heterogeneous and non constant mean. After the first difference, domestic credit attains stationary properties as the p-value is less than 0.05, thus reject the null hypothesis of non-stationary. Monthly domestic credit is of integrated of order 1 ie I(1) thus the value of d in ARIMA(p,d,q) is 1.

Box and Jenkins proposed autocorrelation function (ACF) and partial autocorrelation function (PACF) to generate empirical autocorrelations pattern. The formula for ACF ($\rho_h$) and PACF ($\phi_{h,h}$) are given as in equation (2.14) and (2.15) respectively.

$$ \rho_h = corr(y_t, y_{t-h}) = \frac{\gamma_h}{\gamma_0} \qquad (2.14) $$

$$ \phi_{h,h} = cov(y_t, y_{t+h} | y_{t+1}, y_{t+2}, \dots, y_{t+h-1}) \quad (2.15) $$

Where $h = 1, 2, 3, \dots, n-1$, $\gamma_h = cov(y_t, y_{t-h})$ and $\gamma_0$ is the covariance at lag zero. The behavior of ACF for AR(p) is gradual tail off while for MA(q) it cut off at lag q. On the other hand, PACF for AR(P) cuts off at lags q while for MA(q) there is a gradual tail off.

From Fig. 2 (a), ACF tips off at lag 0 and there is a significant spike at lag 4. Similarly, PACF tips off at lag 0 with significant spike at lag 9 as shown in Fig. 2 (b). This is an indication of a seasonal component in domestic credit. The optimal model considering the ACF and PACF is ARIMA(0,1,0)(1,0,0)$_{12}$.

## (b) Model estimation

Model estimation involves estimating the model parameter corresponding to the moving average process, the autoregressive process and the seasonal process, with the information score for the model included. The parameters are estimated maximizing the function (Hyndman and Athanasopoulos [28]);

$$ L^*(Y_t | Y_{t-1}, \delta_0) \qquad (2.16) $$

where $L^*$ is the conditional likelihood function without the constant terms and $\delta_0 = (\phi, \theta)$

Information criterion is a technique for selecting a model from a finite set of model. Akaike's information criterion (AIC), corrected Akaike's information criterion ($AIC_c$) and Bayesian information criterion (BIC) are considered

in this study. The better model fit is the one that has lower values of AIC and BIC. For any given model, the AIC is given as

$$ AIC = -2\log L(\hat{\theta}) + 2k \qquad (2.17) $$

where $\log L(\hat{\theta})$ is the maximized log-likelihood function with k parameter and t sample data points. Corrected AIC is given as;

$$ AIC_c = AIC + \frac{2k(k+1)}{n-k-1} \qquad (2.18) $$

Similarly, for any model the BIC is given as

$$ BIC = -2\log L(\hat{\theta}) + k\log(t) \qquad (2.19) $$

Three measure of accuracy are considered, namely; namely mean absolute error (MAE), root mean square error (RMSE) and mean average absolute error (MAPE) formulated as shown in equations (2.20), (2.21) and (2.22) respectively.

$$ MAE = \frac{1}{n} \sum_{i=1}^{n} |e_i| \qquad (2.20) $$

$$ RMSE = \sqrt{\frac{\sum_{i=1}^{n} e_i^2}{n}} \qquad (2.21) $$

$$ MAPE = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{e_i}{y_i} \right| \qquad (2.22) $$

The auto.arima function in forecast package in R software, which returns the best ARIMA model according to AIC, $AIC_c$ and BIC values based on step-wise algorithm, is used to return the best model. To model domestic credit, ARIMA(2,1,2)(1,0,0)$_{12}$ is the best fit. The parameter estimates are as shown in table 2. The estimated model has a white noise of 0.0132 standard deviation and a log-likelihood statistic of 697.43. From the measure of accuracy result, on average the fitted model is less than one percent off the observed values.

## (c) diagnostic test

ARIMA model residual analysis involves autocorrelation, heteroscedasticity and normality tests. Normality test uses Ljung-Box test statistics given as

$$ Q(m) = n(n+2) \sum_{k=1}^{m} \frac{r_k^2}{n-k} \qquad (2.23) $$

where n is the sample size, $r_k^2$ is autocorrelation of sample at k lags and m is the lag order. Autocorrelation test is performed by residual ACF test while heteroscedasticity test is performed by
standardized residual plot. The diagnostic test results are as shown in figure 3. The standardized residual plot shows homoscedasticity in the data set. Residual ACF

shows no significant autocorrelation and the Ljung-Box test p-values are all well above 0.05 implying they are non significant.

<figure><img src="image_4.png" /><figcaption>Fig. 2. First difference ACF and PACF</figcaption></figure>

<table><caption>Table 2. ARIMA model estimation</caption><thead><tr><th></th><th colspan="6">parameters</th></tr></thead><tbody><tr><th colspan="7" style="text-align: center;">a</th></tr><tr><th></th><th>ar1</th><th>ar2</th><th>ma1</th><th>ma2</th><th>sar1</th><th>drift</th></tr><tr><th>estimate</th><td>-1.2170</td><td>-0.8569</td><td>1.1378</td><td>0.7340</td><td>0.1603</td><td>0.0114</td></tr><tr><th>s.e</th><td>0.1189</td><td>0.0840</td><td>0.1572</td><td>0.1078</td><td>0.0683</td><td>0.0009</td></tr><tr><th colspan="7" style="text-align: center;">b</th></tr><tr><th></th><th>σ<sup>2</sup></th><th>log likelihood</th><th>AIC</th><th>AICc</th><th>BIC</th><th></th></tr><tr><th></th><td>0.0002</td><td>698.43</td><td>-1382.86</td><td>-1382.37</td><td>-1358.52</td><td></td></tr><tr><th colspan="7" style="text-align: center;">c</th></tr><tr><th></th><th>RMSE</th><th>MAE</th><th>MAPE</th><th></th><th></th><th></th></tr><tr><th></th><td>0.0130</td><td>0.0007</td><td>0.0659</td><td></td><td></td><td></td></tr></tbody></table>

(d) Forecast

Considering an expanded ARIMA (p,1,q) of integrated order one (Brockwell and Davis [29])

$$ (1 - \theta_1 L - \theta_2 L^2 - \dots - \theta_p L^p)(1 - L)y_t = (1 + \phi_1 L + \phi_2 L^2 + \dots + \phi_q L^q)\epsilon_t \quad (2.24) $$

expanding the left hand side of equation (2.24)

$$ [1 - (1 + \theta_1) L + (\theta_1 - \theta_2) L^2 + \dots + (\theta_{p-1} - \theta_p) L^p + \theta_p L^{p+1}] y_t = (1 + \phi_1 L + \phi_2 L^2 + \dots + \phi_q L^q) \epsilon_t \quad (2.25) $$

expanding both sides of equation (2.25)

$$ y_t - (1 + \theta_1)y_{t-1} + (\theta_1 - \theta_2)y_{t-2} + \dots + (\theta_{p-1} - \theta_p)y_{t-p} + \theta_p y_{t-p+1} = \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.26) $$
standardized residual plot. The diagnostic test results are as shown in figure 3. The standardized residual plot shows homoscedasticity in the data set. Residual ACF

shows no significant autocorrelation and the Ljung-Box test p-values are all well above 0.05 implying they are non significant.

<figure><img src="image_4.png" /><figcaption>Fig. 2. First difference ACF and PACF</figcaption></figure>

<table><caption>Table 2. ARIMA model estimation</caption><thead><tr><th></th><th colspan="6">parameters</th></tr></thead><tbody><tr><th colspan="7" style="text-align: center;">a</th></tr><tr><th></th><th>ar1</th><th>ar2</th><th>ma1</th><th>ma2</th><th>sar1</th><th>drift</th></tr><tr><th>estimate</th><td>-1.2170</td><td>-0.8569</td><td>1.1378</td><td>0.7340</td><td>0.1603</td><td>0.0114</td></tr><tr><th>s.e</th><td>0.1189</td><td>0.0840</td><td>0.1572</td><td>0.1078</td><td>0.0683</td><td>0.0009</td></tr><tr><th colspan="7" style="text-align: center;">b</th></tr><tr><th></th><th>σ<sup>2</sup></th><th>log likelihood</th><th>AIC</th><th>AICc</th><th>BIC</th><th></th></tr><tr><th></th><td>0.0002</td><td>698.43</td><td>-1382.86</td><td>-1382.37</td><td>-1358.52</td><td></td></tr><tr><th colspan="7" style="text-align: center;">c</th></tr><tr><th></th><th>RMSE</th><th>MAE</th><th>MAPE</th><th></th><th></th><th></th></tr><tr><th></th><td>0.0130</td><td>0.0007</td><td>0.0659</td><td></td><td></td><td></td></tr></tbody></table>

(d) Forecast

Considering an expanded ARIMA (p,1,q) of integrated order one (Brockwell and Davis [29])

$$ (1 - \theta_1 L - \theta_2 L^2 - \dots - \theta_p L^p)(1 - L)y_t = (1 + \phi_1 L + \phi_2 L^2 + \dots + \phi_q L^q)\epsilon_t \quad (2.24) $$

expanding the left hand side of equation (2.24)

$$ [1 - (1 + \theta_1) L + (\theta_1 - \theta_2) L^2 + \dots + (\theta_{p-1} - \theta_p) L^p + \theta_p L^{p+1}] y_t = (1 + \phi_1 L + \phi_2 L^2 + \dots + \phi_q L^q) \epsilon_t \quad (2.25) $$

expanding both sides of equation (2.25)

$$ y_t - (1 + \theta_1)y_{t-1} + (\theta_1 - \theta_2)y_{t-2} + \dots + (\theta_{p-1} - \theta_p)y_{t-p} + \theta_p y_{t-p+1} = \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.26) $$
<table><caption>Table 3. Banks’ domestic credit forecast results</caption><thead><tr><th>Time</th><th>domestic credit</th><th>95% lower bound</th><th>95% upper bound</th><th>Δ %</th></tr></thead><tbody><tr><td>Jan 2024</td><td>7117196</td><td>6935394</td><td>7303764</td><td>1.217</td></tr><tr><td>Feb 2024</td><td>7203431</td><td>6954456</td><td>7461320</td><td>1.212</td></tr><tr><td>Mar 2024</td><td>7279820</td><td>6979666</td><td>7592881</td><td>1.060</td></tr><tr><td>Apr 2024</td><td>7356737</td><td>7002531</td><td>7728860</td><td>1.057</td></tr><tr><td>May 2024</td><td>7433621</td><td>7039242</td><td>7850095</td><td>1.045</td></tr><tr><td>Jun 2024</td><td>7512585</td><td>7077989</td><td>7973866</td><td>1.062</td></tr><tr><td>Jul 2024</td><td>7604214</td><td>7127893</td><td>8112365</td><td>1.210</td></tr><tr><td>Aug 2024</td><td>7689815</td><td>7179454</td><td>8236456</td><td>1.126</td></tr><tr><td>Sep 2024</td><td>7774258</td><td>7227137</td><td>8362799</td><td>1.099</td></tr><tr><td>Oct 2024</td><td>7859166</td><td>7276852</td><td>8488079</td><td>1.092</td></tr><tr><td>Nov 2024</td><td>7955806</td><td>7340911</td><td>8622206</td><td>1.230</td></tr><tr><td>Dec 2024</td><td>8039222</td><td>7389962</td><td>8745525</td><td>1.048</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Model diagnostics</figcaption></figure>

Making $y_t$ the subject of the formula

$$y_t = (1 + \theta_1)y_{t-1} - (\theta_1 - \theta_2)y_{t-2} - \dots - (\theta_{p-1} - \theta_p)y_{t-p} - \theta_p y_{t-p+1} + \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.27)$$
<table><caption>Table 3. Banks’ domestic credit forecast results</caption><thead><tr><th>Time</th><th>domestic credit</th><th>95% lower bound</th><th>95% upper bound</th><th>Δ %</th></tr></thead><tbody><tr><td>Jan 2024</td><td>7117196</td><td>6935394</td><td>7303764</td><td>1.217</td></tr><tr><td>Feb 2024</td><td>7203431</td><td>6954456</td><td>7461320</td><td>1.212</td></tr><tr><td>Mar 2024</td><td>7279820</td><td>6979666</td><td>7592881</td><td>1.060</td></tr><tr><td>Apr 2024</td><td>7356737</td><td>7002531</td><td>7728860</td><td>1.057</td></tr><tr><td>May 2024</td><td>7433621</td><td>7039242</td><td>7850095</td><td>1.045</td></tr><tr><td>Jun 2024</td><td>7512585</td><td>7077989</td><td>7973866</td><td>1.062</td></tr><tr><td>Jul 2024</td><td>7604214</td><td>7127893</td><td>8112365</td><td>1.210</td></tr><tr><td>Aug 2024</td><td>7689815</td><td>7179454</td><td>8236456</td><td>1.126</td></tr><tr><td>Sep 2024</td><td>7774258</td><td>7227137</td><td>8362799</td><td>1.099</td></tr><tr><td>Oct 2024</td><td>7859166</td><td>7276852</td><td>8488079</td><td>1.092</td></tr><tr><td>Nov 2024</td><td>7955806</td><td>7340911</td><td>8622206</td><td>1.230</td></tr><tr><td>Dec 2024</td><td>8039222</td><td>7389962</td><td>8745525</td><td>1.048</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Model diagnostics</figcaption></figure>

Making $y_t$ the subject of the formula

$$y_t = (1 + \theta_1)y_{t-1} - (\theta_1 - \theta_2)y_{t-2} - \dots - (\theta_{p-1} - \theta_p)y_{t-p} - \theta_p y_{t-p+1} + \epsilon_t + \phi_1 \epsilon_{t-1} + \phi_2 \epsilon_{t-2} + \dots + \phi_q \epsilon_{t-q} \quad (2.27)$$
For $t = T + 1$

$$y_{T+1} = (1 + \theta_1)y_T - (\theta_1 - \theta_2)y_{T-1} - \dots - (\theta_{p-1} - \theta_p)y_{T-p+1} - \theta_p y_{T-p+2} + \epsilon_{T+1} + \phi_1 \epsilon_T + \phi_2 \epsilon_{T-1} + \dots + \phi_q \epsilon_{T-q+1} \quad (2.28)$$

Forecast to h step ahead is given as shown in equation (2.28)

$$y_{T+h|T} = (1 + \theta_1)y_{T+h-1} - (\theta_1 - \theta_2)y_{T+h-2} - \dots - (\theta_{p-1} - \theta_p)y_{T+h-p} - \theta_p y_{T+h-p+1} + \epsilon_{T+h} + \phi_1 \epsilon_{T+h-1} + \phi_2 \epsilon_{T+h-2} + \dots + \phi_q \epsilon_{T+h-q} \quad (2.29)$$

For the error terms only the previous observed residual $\epsilon_{T+h-1}$ is included as all the other errors terms are replaced by zero, reducing equation (2.29) to

$$y_{T+h|T} = (1 + \theta_1)y_{T+h-1} - (\theta_1 - \theta_2)y_{T+h-2} - \dots - (\theta_{p-1} - \theta_p)y_{T+h-p} - \theta_p y_{T+h-p+1} + \phi_1 \epsilon_{T+h-1} \quad (2.30)$$

Forecast values form January 2024 to December 2024 are as shown in table 3 and Fig. 3, with a 95% confidence interval. Domestic credit sector will experience a rise in credit value in the years 2024. The values will range from 7.117 to 8.039 Trillions by December 2024. The projected rate of increase will approximately more than 1 percent but less than 1.3 percent.

Domestic credit

<figure><img src="image_6.png" /><figcaption>Fig. 4. Domestic credit forecast</figcaption></figure>

# 3 DISCUSSION AND CONCLUSION

The objective of the study was to analyze domestic credit growth, its times series property and its expected value and trend. Generally, there has been a continuous increase in domestic credit from the period 2004 to 2023. Box-Jenkins framework was used to estimate the ARIMA model. In the first step, Unit root test

and correlogram analysis were conducted. Domestic credit is non stationary in level though its of integration order one ie I(1). Both ACF and PACF tips off at lag 0 implying p and q parameters equal to zero. There are significant spikes in ACF and PACF at 4 and 9 respectively. This suggest the presence of seasonality component in the ARIMA model. In the second step, ARIMA(2,1,2)(1,0,0)$_{12}$ is estimated as the best fit for
For $t = T + 1$

$$y_{T+1} = (1 + \theta_1)y_T - (\theta_1 - \theta_2)y_{T-1} - \cdots - (\theta_{p-1} - \theta_p)y_{T-p+1} - \theta_p y_{T-p+2} + \epsilon_{T+1} + \phi_1 \epsilon_T + \phi_2 \epsilon_{T-1} + \cdots + \phi_q \epsilon_{T-q+1} \quad (2.28)$$

Forecast to h step ahead is given as shown in equation (2.28)

$$y_{T+h|T} = (1 + \theta_1)y_{T+h-1} - (\theta_1 - \theta_2)y_{T+h-2} - \cdots - (\theta_{p-1} - \theta_p)y_{T+h-p} - \theta_p y_{T+h-p+1} + \epsilon_{T+h} + \phi_1 \epsilon_{T+h-1} + \phi_2 \epsilon_{T+h-2} + \cdots + \phi_q \epsilon_{T+h-q} \quad (2.29)$$

For the error terms only the previous observed residual $\epsilon_{T+h-1}$ is included as all the other errors terms are replaced by zero, reducing equation (2.29) to

$$y_{T+h|T} = (1 + \theta_1)y_{T+h-1} - (\theta_1 - \theta_2)y_{T+h-2} - \cdots - (\theta_{p-1} - \theta_p)y_{T+h-p} - \theta_p y_{T+h-p+1} + \phi_1 \epsilon_{T+h-1} \quad (2.30)$$

Forecast values form January 2024 to December 2024 are as shown in table 3 and Fig. 3, with a 95% confidence interval. Domestic credit sector will experience a rise in credit value in the years 2024. The values will range from 7.117 to 8.039 Trillions by December 2024. The projected rate of increase will approximately more than 1 percent but less than 1.3 percent.

### Domestic credit

<figure><img src="image_6.png" /><figcaption>Fig. 4. Domestic credit forecast</figcaption></figure>

## 3 DISCUSSION AND CONCLUSION

The objective of the study was to analyze domestic credit growth, its times series property and its expected value and trend. Generally, there has been a continuous increase in domestic credit from the period 2004 to 2023. Box-Jenkins framework was used to estimate the ARIMA model. In the first step, Unit root test

and correlogram analysis were conducted. Domestic credit is non stationary in level though its of integration order one ie I(1). Both ACF and PACF tips off at lag 0 implying p and q parameters equal to zero. There are significant spikes in ACF and PACF at 4 and 9 respectively. This suggest the presence of seasonality component in the ARIMA model. In the second step, ARIMA(2,1,2)(1,0,0)$_{12}$ is estimated as the best fit for
the sample period. The model has a high level of error accuracy as fitted values are less than percent of the observed values. In the model diagnostic step, all assumption of ARIMA analysis are meet' there is no hetetroscedasticity, no significant auto-correlation and insignificant Ljung-Box test p-values. The estimated model is used to forecast monthly value over a forecast horizon of twelve period.

From the study, domestic credit has a varying constant and mean. Thus, its highly influenced by economic shocks that it experiences at any given time. Considering the sample period, ARIMA model with p,d,q parameter corresponding to 2,1,2 and seasonal parameter 1,0,0 for P,D,Q respectively is the best for modeling and forecasting. Its projected that domestic credit will continue to rise in the year 2024 through to December. The expected domestic credit value in December 2024 is 8.039 Trillions with a confidence interval from 7.389 to 8.746 Trillions. Kenya government should put in place monetary policy that favors bank credit growth and competition in the banking sector. Well managed credit growth will enable Kenya's economy to benefit especially for the macroeconomic variables that interact positively such as money supply, GDP, trade openness and interest rates.

COMPETING INTERESTS

Author has declared that no competing interests exist.

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[17] Di Giovanni J, Kalemli-Özcan Ş, Ulu MF, Baskaya YS. International spillovers and local credit cycles. The Review of Economic Studies. 2022; 89(2): 733-773.
the sample period. The model has a high level of error accuracy as fitted values are less than percent of the observed values. In the model diagnostic step, all assumption of ARIMA analysis are meet' there is no hetetroscedasticity, no significant auto-correlation and insignificant Ljung-Box test p-values. The estimated model is used to forecast monthly value over a forecast horizon of twelve period.

From the study, domestic credit has a varying constant and mean. Thus, its highly influenced by economic shocks that it experiences at any given time. Considering the sample period, ARIMA model with p,d,q parameter corresponding to 2,1,2 and seasonal parameter 1,0,0 for P,D,Q respectively is the best for modeling and forecasting. Its projected that domestic credit will continue to rise in the year 2024 through to December. The expected domestic credit value in December 2024 is 8.039 Trillions with a confidence interval from 7.389 to 8.746 Trillions. Kenya government should put in place monetary policy that favors bank credit growth and competition in the banking sector. Well managed credit growth will enable Kenya's economy to benefit especially for the macroeconomic variables that interact positively such as money supply, GDP, trade openness and interest rates.

COMPETING INTERESTS

Author has declared that no competing interests exist.

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© Copyright (2024): Author(s). The licensee is the journal publisher. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Peer-review history:

The peer review history for this paper can be accessed here:

https://www.sdiarticle5.com/review-history/115407
[18] Igan D, Kutan AM, Mirzaei A. The real effects of capital inflows in emerging markets. Journal of Banking & Finance. 2020; 119: 105933.

[19] Noreen A, Asif R, Nisar S, Qayyum N. Model building and forecasting of bank credit to public and private sector. Universal Journal of Accounting and Finance. 2017; 5(4): 73-77.

[20] Dinh DV. Forecasting domestic credit growth based on ARIMA model: Evidence from Vietnam and China. Management Science Letters. 2020; 10(5): 1001-1010.

[21] Obeng-Amponsah W, Zehou S, Dey EA. Using exponential smoothing method in forecasting domestic credit to private sector of Ghana. Journal on Innovation and Sustainability RISU. 2019; 10(3).

[22] Kiriga B, Chacha T, Omany D. Assessing the Impact of Private Sector Credit on Economic Growth in Kenya. Kenya Institute for Public Policy Research and Analysis. 2020.

[23] Kibet K, Cheboi J, Agak T. Credit to private sector, investor protection, foreign exchange rate, corruption perception and economic growth nexus among comesa countries. Econ Res. 2022; 6(3): 108-122.

[24] Box GEP, Jenkins GM. Time Series Analysis, Forecasting and Control. San Francisco, California: Holden-Day. 1976.

[25] Dickey DA, Fuller WA. Distributions of the estimators for autoregressive time series with a unit root. Journal of American Statistical Association. 1979; 74(366): 427-431.

[26] Dickey DA, Fuller WA. Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica. 1981; 49(4): 1057-1072.

[27] Phillips PCB, Perron P. Testing for a unit root in time series regression. Biometrika. 1998; 75(2): 335-346.

[28] Hyndman RJ, Athanasopoulos G. Forecasting: principles and practice. OTexts. 2018.

[29] Brockwell PJ, Davis RA. (Eds.). Introduction to time series and forecasting. New York, NY: Springer New York. 2002.

© Copyright (2024): Author(s). The licensee is the journal publisher. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Peer-review history:

The peer review history for this paper can be accessed here:

https://www.sdiarticle5.com/review-history/115407