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

ifip

International Federation for Information Processing

This document is the original author manuscript of a paper submitted to an IFIP
conference proceedings or other IFIP publication by Springer Nature. As such, there
may be some differences in the official published version of the paper. Such
differences, if any, are usually due to reformatting during preparation for publication or
minor corrections made by the author(s) during final proofreading of the publication
manuscript.
# Data Analytics of Climate using the PCA-VARI Model
## Case Study in West Java, Indonesia

Devi Munandar¹[0000-0002-5766-1139], Putri Monika¹[0009-0009-9149-2250], Ajeng Berliana Sal-sabila¹[0009-0009-3355-6105], Frida Helen²[0000-0002-2310-2355], Atje Setiawan Abdullah²[0000-0002-3877-3522], and Budi Nurani Ruchjana¹[0000-0001-7580-604X]

¹ Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia

² Department of Computer Science, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia
budi.nurani@unpad.ac.id

**Abstract.** Climate change occurs in the atmosphere over a long period due to the influence of the sun, oceans, clouds, ice, land, and living organisms on each other. This research used the Principal Component Analysis (PCA) model compounded with Vector Autoregressive Integrated (VARI) called the PCA-VARI model to determine climate change. PCA reduces correlated climate data to uncorrelated data expressed as main components containing a linear combination of initial variables. In the time series model, a non-stationary multivariate comprises more than two variables that influence each other, using differencing processes. A variety of two models was used simultaneously to forecasting future climate data. Analysis of climate parameters uses ten measurements variable located in five areas, namely Lembang, Bogor, Tasikmalaya, Sukabumi, and Indramayu, for twenty years, using POWER NASA Agro-climatology datasets. The methodology follows the Knowledge Discovery in Databases (KDD) in data mining for integrated PCA with VARI and post-processing using visualization by Impulse Response Function (IRF). The result of forecasting in the PCA-VARI model using IRF in the next six months showed that the effect of location climate on the response of other regions with changes in standard deviation is similar to adjacent locations. Meanwhile, the responses obtained varied based on the observation time for the five areas that are not close.

**Keywords:** PCA-VARI Model, Climate, Forecasting, IRF, KDD

## 1 Introduction

Changes in the atmosphere are subject to long-term restrictions, usually from minutes to months. Weather and climate have different meanings in climatology with time as their dissimilarity. While the weather is a change or state of the atmosphere within a
short period, climate occurs over a long time due to temperature, humidity, rainfall, atmospheric pressure, and others. This phenomenon can be interpreted as a stochastic process with a sequence of place and time of climate variables and large data. Therefore, the Principal Component Analysis (PCA) process is needed to reduce variables through linear combinations or orthogonal transformations, such as marine climate applications [1]. The correlation between climate variables and time index allows univariate or multivariate modeling also need to be analyzed. This is in addition to the daily and monthly observation of various climate variables that affect weather changes. Knowledge Discovery in Database (KDD), with a theoretically three-step approach, namely preprocessing, data mining, and post-processing, is used to model climate variables. Meanwhile, those with a fairly high correlation can be modeled using Vector Autoregressive (VAR) or Vector Autoregressive integrated (VARI) as the implementation of the multivariate time series model [2]. The effect of the main climate variability, such as rainfall, humidity, and temperature, can be modeled to analyze the variance decomposition that causes an increase in malaria sufferers [3] [4].

In the scope of econometrics, the integration of PCA and VAR has significant meaning on human life caused by the influence of the climate, financial system, environmental pollution, and social media. The environmental effects influenced by vehicle exhaust emissions as a subsystem significantly affect development as an interaction with other subsystems. Integrating the two models is helpful and acts as a model that provides recommendations for these problems [5].

This study aims to combine Principal Components with integrated Vector Autoregressive through the KDD process in data mining [6]. Climate data in the West Java region of Indonesia were measured to obtain a multivariate time series model with a smaller number of variables. The acquisition of a new model from the combination of the two makes it easier to forecast and interpret the results. The Principal Component, an orthogonal transformation of the initial variable, performs the reduction process without losing much information. The percentage of cumulative variance, especially in the first Principal Component, is new data as input to the VARI model [7][8]. Previous research outcomes explained that this examination uses this integrated model to evaluate correlation variables in this region's climate data. It contributes to the influence of the location climate for recommending community needs, such as planting season, harvest time, and analysis of disaster risk reduction, especially floods.

# 2 Research Methods

## 2.1 KDD Methods in Data Mining

Data mining is a technique for analyzing big data to obtain information through statistical and mathematical methods through artificial intelligence. This method also uses nontrivial processes to determine patterns between datasets and make predictions as a decision support system [9]. The implementation process of combining statistical and multivariate models as one of the data mining functions can be seen in Fig. 1 [10]. The two main functions of data mining are descriptive and predictive, which is an
analysis of the behavior and patterns of data to be better understood and obtain information through technology [11][12]. In the KDD stage, an in-depth data mining process is used to determine hidden patterns from climate datasets. This stage starts with preprocessing the dataset to cleaning and transforming it daily to monthly. The data mining process integrates PCA and VARI to produce a new model with the Principal Component dataset. In the end, post-processing, as information generated in the previous stage, is visualized and interpreted as a decision support recommendation.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Knowledge Discovery in Databases Process</figcaption></figure>

## 2.2 PCA-VARI Model

PCA focuses on variable reduction, while VARI is a multivariate time series technique as stated in the following sub-sections.

**Principal Component Analysis.** Before the modeling process is conducted, the climate dataset must undergo a statistical test using the Kaiser-Meyer-Olkin (KMO) Test for Sampling Adequacy examination to determine the correlation between variables [13]. PCA specifically indicates the covariance matrix for climate variables through orthogonal transformations for its reduction [14]. It comprises *p* *k* components, and by accomplishing PCA *p* > *k*. This indicates that *k* can clarify and change the main variables, which have the number *p* [15]. The vector *X*' = {*X*₁, *X*₂, *X*₂, ..., *X*ₙ} and covariance matrix Σ with *p* eigenvalues λ₁ ≥ λ₂ ≥ λ₃ ≥ ... ≥ λₚ ≥ 0 indicate the occurrence of an orthogonal transformation *p* as follows:

$$ \eta_1 = \mathbf{a}'_1 \mathbf{X} = a_{11}X_1 + a_{12}X_2 + \dots + a_{1p}X_p \quad (1) $$

$$ \eta_p = \mathbf{a}'_p \mathbf{X} = a_{p1}X_1 + a_{p2}X_2 + \dots + a_{pp}X_p $$

*p* is made up of linear combinations, such that every variable is uncorrelated or linearly unbiased with the aid of taking only *k*. Therefore, the obtained Var(ηᵢ) = aᵢ'Σaᵢ and Cov(ηᵢ, ηₖ) = aᵢ'Σaₖ with *i*, *k* = 1, 2, ..., *p*. To obtain the *i*th principal component, a delegated linear combination maximizes Var(aᵢ'X) below the condition aᵢ'aᵢ = 1 and all covariates for *k* < *i* = 0 or Cov(aᵢ'X, aₖ'X) = 0 for *k* < *i*. Linear algebra [16] is described if X' = {*X*₁, *X*₂, *X*₂, ..., *X*ₙ} with a covariance matrix Σ comprising pairs of eigenvalues and eigenvectors (λ₁, a₁), (λ₂, a₂), ..., (λₚ, aₚ) where λ₁ ≥ λ₂ ≥ λ₃ ≥ ... ≥ λₚ ≥ 0 in addition to η₁ = a₁'X, η₂ = a₂'X, ..., ηₚ = aₚ'X
is the first principal component, followed by
$\sigma_{11} + \sigma_{22} + \dots + \sigma_{pp} = \sum_{i=1}^{p} \mathrm{Var}(X_i) = \lambda_1 + \lambda_2 \ge \lambda_+ \ge \dots + \lambda_p = \sum_{i=1}^{p} \mathrm{Var}(\eta_i)$ the
quantify of the general variance for the $k^{th}$ principal component is
$\lambda_k / \lambda_1 + \lambda_2 + \dots + \lambda_p$.

Vector Autoregressive Integrated (VARI).

The method used in VARI modeling to obtain optimal results for forecasting station-
ary data is the Box-Jenkin procedure. It generally consists of the following steps: (i)
Identification process to ensure the data is stationary in the mean and variance. For
non-stationary data, differencing processes and Box-Cox transformations are carried
out until it becomes stationary. (ii) Estimation of model parameters using Ordinary
Least Squared (OLS) or Maximum Likelihood Estimation (MLE). (iii) Diagnostic
tests to confirm the model meets the criteria by testing the residuals of the modeling
results. These conditions will return to process (i) if they are still not met until fore-
casting is considered possible [17].

Stationary data is a simple assumption that must be met in VARI modeling. Further
analysis can be obtained assuming the statistical significance of the data is not deter-
mined at the unit root with the condition that it does not have criteria for seasonal
fluctuations. The Augmented Dickey-Fuller test can meet the following autoregres-
sive criteria: $\Delta Z_{t-p}$ in the model with $\gamma = 0$

$\Delta Z_t = Z_t - Z_{t-1} = \alpha + \beta t + \gamma Z_{t-1} + \delta_1 \Delta Z_{t-1} + \delta_2 \Delta Z_{t-2} + \dots + \delta_p \Delta Z_{t-p} \quad (2) Z_t$ is
series data, used to obtain $\Delta Z_t$ to $t$ and $Z_{t-1}$ to $\gamma \neq 0$ through linear and verification
processes. If there is no unit root, $-1 < 1 + \gamma < 1$ the procedure may be stationary [18].
The presence of a unit root indicates that the data is not stationary in the mean, hence
$H_0: \phi = 1$. Meanwhile, if no unit root indicates stationary in the mean, $H_1: \phi < 1$.

Rejection of the *p*-value at a significance level of less than 0.05 [19] indicates that the selection of the Box-Cox transformation is required for data that is not stationary in the variance. The determination of exponential lambda (λ) on the transformation is considered to meet the criteria if it has a value of more than 1. However, some preliminary studies stated that references are between -5 to 5 [20].

Evaluation is further needed to determine the accuracy level of modeling climate
data using VARI by selecting the lag value in accordance with the Schwarz Infor-
mation Criterion (SIC) [21]. Meanwhile, variable estimation using the Maximum
Likelihood Estimation (MLE) [22] is a composite probability density function to ob-
tain parameter estimates with regression values correlated using random error values
in a normal distribution.

Assuming the Vector Autoregressive model is not stationary, then the differencing
process is executed *k* times until the data is stationary, and the VARI(*p*,*k*) model is
obtained. If the coefficients of *p* and *k* are 1, respectively, then the VARI(1,1) matrix
is as follows:
$$ \begin{bmatrix} \dot{Z}_{1,t} \\ \dot{Z}_{2,t} \\ \vdots \\ \dot{Z}_{M,t} \end{bmatrix} - \begin{bmatrix} \dot{Z}_{1,t-1} \\ \dot{Z}_{2,t-1} \\ \vdots \\ \dot{Z}_{M,t-1} \end{bmatrix} = \begin{bmatrix} \phi_{11} & \phi_{12} & \cdots & \phi_{1M} \\ \phi_{21} & \phi_{22} & \cdots & \phi_{2M} \\ \vdots & \vdots & \ddots & \vdots \\ \phi_{M1} & \phi_{M2} & \cdots & \phi_{MM} \end{bmatrix} \begin{pmatrix} \begin{bmatrix} \dot{Z}_{1,t-1} \\ \dot{Z}_{2,t-1} \\ \vdots \\ \dot{Z}_{M,t-1} \end{bmatrix} - \begin{bmatrix} \dot{Z}_{1,t-2} \\ \dot{Z}_{2,t-2} \\ \vdots \\ \dot{Z}_{M,t-2} \end{bmatrix} \\ + \begin{bmatrix} e_{1,t} \\ e_{2,t} \\ \vdots \\ e_{M,t} \end{bmatrix} $$

or equal to

$$ \dot{Z}_t - \dot{Z}_{t-1} = \mathbf{\Phi}_1(\dot{Z}_{t-1} - \dot{Z}_{t-2}) + \mathbf{e}(t) \quad (3) $$

with error value is normal distribution, i.e. $e_t \sim N(0, \sigma^2)$, and $\dot{Y}_t = \dot{Z}_{1,t} - \dot{Z}_{1,t-1}$, then satisfies with $t = 2, 3, ..., T$ and VARI equation

$$ \dot{\mathbf{Y}}_{t((M \times (T-1)) \times 1)} = \dot{\mathbf{Y}}_{t-1((M \times (T-1)) \times (M \times M))} \mathbf{\Phi}_{((M \times M) \times 1)} + \mathbf{e}_{t((M \times (T-1)) \times 1)} \quad (4) $$

The obtained model is then tested by analyzing the residual series using white noise on the resulting parameters, assuming there is no random correlation with zero mean and constant detected variance. The null hypothesis test was also conducted on the uncorrelated residual ACF sample as a diagnostic test using the Ljung-Box.

As a statistical procedure useful for observing time series, the Granger test has a causal relationship between modeled climate variables [23]. Assuming X and Y are stationary series, to determine the ability of X Granger to produce Y can be defined as follows:

$$ y_t = \alpha_0 + \sum_{i=1}^{p} \alpha_i y_{t-i} + \sum_{j=1}^{q} \beta_i x_{t-j} + a_t \text{ and } y_t = \delta_0 + \sum_{i=1}^{p} \delta_i y_{t-i} + e_t \text{ (null hypothesis model).} $$

The impulse response function (IRF) is the feedback of the VARI model in response to some changes between the variables. IRF is used to examine the effect of a shock or a variable on itself and others from modeling in both short and long periods. According to the VARI model described in Equation (3)

$$ \Upsilon_t = \mu + \varepsilon_t + \Theta_1 \varepsilon_{t-1} + \Theta_2 \varepsilon_{t-2} + \Theta_3 \varepsilon_{t-3} + \dots $$

the $\Theta_s$ matrix is interpreted as

$$ \Theta_s = \frac{\partial \Upsilon_{t+s}}{\partial \varepsilon'_t} \quad (5) $$

where i denotes row, and j represents column for recognition of $\Theta_s$ intensifying unit of jth variable at date t ($\varepsilon_{jt}$) to value of ith at a time t + s ($\Upsilon_{i,t+s}$). The ith row, jth column members of $\Theta_s$, known as the IRF function, also continuously keeps all other variables.
# 3 Result and Discussion

## 3.1 Preprocessing of Data Mining

Before creating the PCA-VARI model, the data were first collected from climate resources of POWER NASA [27] consisting of Lembang, Bogor, Tasikmalaya, Sukabumi, and Indramayu West Java province of Indonesia from 2001 to 2020 using the daily measurement time [28].

<table><caption>**Table 1:** Variables for Lembang, Bogor, Tasikmalaya, Sukabumi, and Indramayu regions</caption><thead><tr><th>Lembang (LM), Bogor (BG), Tasikmalaya (TS), Sukabumi (SM), Indramayu (IN)</th></tr></thead><tbody><tr><td>LM<sub>1</sub>, BG<sub>1</sub>, TS<sub>1</sub>, SM<sub>1</sub>, IN<sub>1</sub> = UV Index (uvi)</td></tr><tr><td>LM<sub>2</sub>, BG<sub>2</sub>, TS<sub>2</sub>, SM<sub>2</sub>, IN<sub>2</sub> = Temperature (tem)</td></tr><tr><td>LM<sub>3</sub>, BG<sub>3</sub>, TS<sub>3</sub>, SM<sub>3</sub>, IN<sub>3</sub> = Dewpoint (dew)</td></tr><tr><td>LM<sub>4</sub>, BG<sub>4</sub>, TS<sub>4</sub>, SM<sub>4</sub>, IN<sub>4</sub> = Solar radiation (sor)</td></tr><tr><td>LM<sub>5</sub>, BG<sub>5</sub>, TS<sub>5</sub>, SM<sub>5</sub>, IN<sub>5</sub> = Humidity (hum)</td></tr><tr><td>LM<sub>6</sub>, BG<sub>6</sub>, TS<sub>6</sub>, SM<sub>6</sub>, IN<sub>6</sub> = Precipitation (pre)</td></tr><tr><td>LM<sub>7</sub>, BG<sub>7</sub>, TS<sub>7</sub>, SM<sub>7</sub>, IN<sub>7</sub> = Air pressure (arp)</td></tr><tr><td>LM<sub>8</sub>, BG<sub>8</sub>, TS<sub>8</sub>, SM<sub>8</sub>, IN<sub>8</sub> = Wind speed (wsp)</td></tr><tr><td>LM<sub>9</sub>, BG<sub>9</sub>, TS<sub>9</sub>, SM<sub>9</sub>, IN<sub>9</sub> = Root soil wetness (rsw)</td></tr><tr><td>LM<sub>10</sub>, BG<sub>10</sub>, TS<sub>10</sub>, SM<sub>10</sub>, IN<sub>10</sub> = Surface root wetness (srw)</td></tr></tbody></table>

Table 1 shows the use of the same measurement variables for each of the five locations from 2001 to 2020 [24]. The variable selection decisions were based on available data indicators in addition to the theoretical research basis and geographic location [25]. Furthermore, Table 1 also shows that eight of the overall variables indicate the climate in general [26]. The root soil wetness (rsw) and surface root wetness (srw) represent agroclimatological variables, which are included in the measurement and can affect each area. Daily data acquisition is aggregated into monthly data for simple modeling and put together in CSV file format to assist in organizing in one locality.

## 3.2 PCA-VARI in Data Mining Process

### Principal Component Recognition for PCA-VARI

The climate data verified in the preprocessing step starts by testing the data's feasibility before calculating to model the correlation value between variables simultaneously using KMO. The results obtained for the five locations were 0.6105, 0.5401, 0.7023, 0.5514, 0.6429, respectively. PCA modeling process can be continued because the test criteria obtained at the correlation of each variable is greater than 0.5.
<table><caption>**Table 2:** Estimation of eigenvalues for five climate locations</caption><thead><tr><th>Principal component</th><th>Eigenvalue (LM)</th><th>Eigenvalue (BG)</th><th>Eigenvalue (TS)</th><th>Eigenvalue (SM)</th><th>Eigenvalue (IN)</th></tr></thead><tbody><tr><td><b>1</b></td><td>4.9866</td><td>4.6862</td><td>5.5478</td><td>4.8586</td><td>5.7213</td></tr><tr><td><b>2</b></td><td>2.0370</td><td>2.0641</td><td>2.0896</td><td>1.9380</td><td>1.9985</td></tr><tr><td><b>3</b></td><td>1.3877</td><td>1.4458</td><td>0.7586</td><td>1.3608</td><td>0.8976</td></tr><tr><td><b>4</b></td><td>0.7657</td><td>0.7988</td><td>0.6530</td><td>0.8597</td><td>0.6560</td></tr><tr><td><b>5</b></td><td>0.4352</td><td>0.5566</td><td>0.4400</td><td>0.5555</td><td>0.3707</td></tr><tr><td><b>6</b></td><td>0.2470</td><td>0.2471</td><td>0.2422</td><td>0.2585</td><td>0.2017</td></tr><tr><td><b>7</b></td><td>0.0896</td><td>0.1228</td><td>0.1886</td><td>0.0896</td><td>0.1170</td></tr><tr><td><b>8</b></td><td>0.0493</td><td>0.0732</td><td>0.0777</td><td>0.0764</td><td>0.0315</td></tr><tr><td><b>9</b></td><td>0.0016</td><td>0.0050</td><td>0.0024</td><td>0.0025</td><td>0.0052</td></tr><tr><td><b>10</b></td><td>0.0003</td><td>0.0005</td><td>0.0001</td><td>0.0004</td><td>0.0005</td></tr></tbody></table>

Based on the results obtained in Table 2, the percentage of the cumulative variability of the main components using the correlation matrix with the minimum achievement exceeding 70% was obtained for the climatic areas of Lembang, Tasikmalaya, and Indramayu. It is explained by two principal components, namely PC1 and PC2, with the proportions of 70.24%, 76.37%, and 77.20%, respectively. Meanwhile, the Bogor, Sukabumi climate region consists of three principal components, namely PC1, PC2, and PC3, with a proportion of 81.96%, and 81.57%, respectively. The proportion of each principal component varies based on the eigenvalues obtained from the correlation matrix. The eigenvectors corresponding to the eigenvalues for each climate location data are linear combinations for PCA modeling. After the eigenvalues are obtained, the eigenvectors are as in Table 3.

<table><caption>**Table 3:** Estimation of eigenvectors for five climate locations</caption><thead><tr><th>Variable of climate</th><th>Eigenvector (PC1-LM)</th><th>Eigenvector (PC1-BG)</th><th>Eigenvector (PC1-TS)</th><th>Eigenvector (PC1-SM)</th><th>Eigenvector (PC1-IN)</th></tr></thead><tbody><tr><td><b>uvi</b></td><td>-0.0768</td><td>-0.0908</td><td>-0.1070</td><td>-0.0808</td><td>-0.0509</td></tr><tr><td><b>tem</b></td><td>0.2259</td><td>-0.1012</td><td>-0.3800</td><td>0.2358</td><td>0.0218</td></tr><tr><td><b>dew</b></td><td>0.4270</td><td>0.4029</td><td>-0.4100</td><td>0.4369</td><td>0.4052</td></tr><tr><td><b>sor</b></td><td>0.3603</td><td>0.2320</td><td>-0.3595</td><td>0.3158</td><td>0.3702</td></tr><tr><td><b>hum</b></td><td>0.3886</td><td>0.4454</td><td>-0.1545</td><td>0.3960</td><td>0.3798</td></tr><tr><td><b>pre</b></td><td>0.3640</td><td>0.3489</td><td>-0.3422</td><td>0.3516</td><td>0.3289</td></tr><tr><td><b>arp</b></td><td>-0.2490</td><td>-0.2738</td><td>0.3080</td><td>-0.2539</td><td>-0.2595</td></tr><tr><td><b>wsp</b></td><td>-0.0324</td><td>0.1992</td><td>0.2815</td><td>-0.0856</td><td>-0.3108</td></tr><tr><td><b>rsw</b></td><td>0.3707</td><td>0.3930</td><td>-0.3296</td><td>0.3708</td><td>0.3648</td></tr><tr><td><b>srw</b></td><td>0.3834</td><td>0.4197</td><td>-0.3509</td><td>0.3969</td><td>0.3825</td></tr></tbody></table>

In Table 3 the variables with the highest positive effect on the first principal component Lembang (PC1-LM), consisted of dew point and humidity in values of 0.4270 and 0.3886. Meanwhile, on the first principal component Bogor (PC1-BG), the variance comprises humidity and surface root wetness in values of 0.4454 and 0.4197. In contrast to the first principal component Tasikmalaya (PC1-TS) dew point and air temperature have a dominant variance contribution of -0.4100 and -0.3800. The
minus sign is an indication of a negative change to the variance. For first principal component, Sukabumi (PC1-SM) dew point and surface root wetness are 0.4369 and 0.3969. Meanwhile, the location of first principal component, Indramayu (PC1-IN), has the highest contribution to the dew point and humidity at values of 0.4052 and 0.3798. The contribution of the principal component for each regional climate location describes the eigenvectors of each location to determine the most variance in dew point and humidity. This indicates that in West Java, the two variables contributed an important role in conditions. The role of surface root wetness is also raised as a contribution representing the principal component, indicating the region is close to the equator. The new dataset can be seen in Fig. 2 through linear combination processes like Equation (1) and used to predict the inter-site climate influence based on PCA-VARI to obtain a seasonal pattern.

## Identifications of PCA-VARI Locations

Stationary model using test Augmented Dickey-Fuller (ADF) and Box-Cox determined the stationary climate data in mean and variance of PC1-LM, PC1-BG, PC1-TS, PC1-SM, PC1-IN respectively as $\gamma_{1,t}, \gamma_{2,t}, \gamma_{3,t}, \gamma_{4,t}, \gamma_{5,t}$. The new variables from Principal Component were tested by applying measurements in two tests, namely i) differencing original non-stationary data for each location; and ii) differencing of new data resulting from the PCA process. The ADF and Box-Cox test values show varying values to analyze the significance of the data assumptions shown in the Table. 4. The significant value used for ADF $\alpha < 0.05$ and Box-Cox $\approx 1$ to view that PCA climate data has changed. The process to stationary performs differencing is used to meet the test significant value limit.

<figure><img src="image_3.png" /><figcaption>**Fig. 2:** New dataset after a principal component process</figcaption></figure>

Table 4 shows that the first principal component data for PC1 of climate locations is not stationary in the average for $\hat{\gamma}_{1,t}$PC1-LM, $\hat{\gamma}_{1,t}$PC1-BG, $\hat{\gamma}_{1,t}$PC1-TS, and $\hat{\gamma}_{1,t}$PC1-SM. Meanwhile, for stationary data in variance where the Box-Cox value is close to 1, $\hat{\gamma}_{1,t}$PC1-IN has a sufficient value. The transformation process is conducted before differencing process at the first level to determine whether the data is stationary. The differencing process has a *p*-value of less than 5% (0.05), hence when it is more than
0.05, H₀ is rejected, indicating data is not stationary, and the Box-Cox value is close to 1.

<table><caption>**Table 4:** First principal component stationary</caption><thead><tr><th rowspan="2">Variable</th><th colspan="2">Without different</th><th colspan="2">With different</th></tr><tr><th>p-value</th><th>Box-Cox</th><th>p-value</th><th>Box-Cox</th></tr></thead><tbody><tr><td>ŷ<sub>1,t</sub>PC1-LM</td><td>0.1742</td><td>0.9995</td><td>0.0001</td><td>0.9993</td></tr><tr><td>ŷ<sub>1,t</sub>PC1-BG</td><td>0.8687</td><td>0.9994</td><td>0.0001</td><td>0.9928</td></tr><tr><td>ŷ<sub>1,t</sub>PC1-TS</td><td>0.3926</td><td>0.6925</td><td>0.0001</td><td>0.9935</td></tr><tr><td>ŷ<sub>1,t</sub>PC1-SM</td><td>0.7858</td><td>0.9992</td><td>0.0001</td><td>0.9894</td></tr><tr><td>ŷ<sub>1,t</sub>PC1-IN</td><td>0.0190</td><td>0.9967</td><td>0.0001</td><td>0.9146</td></tr></tbody></table>

Table 5 shows that selecting the Schwarz Information Criterion (SC) model as the PCA-VARI(1) lag sequence has a minimum value that will be used for modeling. MLE is used to calculate the model coefficients and parameter estimation. The markers in Tables 5 and 6 show the order of the lags with the first-order lag selected using the SC(n) criteria to obtain the minimum value at the significance level of α < 0.05.

<table><caption>**Table 5:** Lag order criteria on the PCA-VARI model</caption><thead><tr><th></th><th>PCA-VARI(1)</th><th>PCA-VARI(2)</th><th>PCA-VARI(3)</th><th>PCA-VARI(4)</th><th>PCA-VARI(5)</th></tr></thead><tbody><tr><td>AIC(n)</td><td>1.2771</td><td>0.9986</td><td>0.8910</td><td>0.8420</td><td>0.7677*</td></tr><tr><td>HQ(n)</td><td>1.7534</td><td>1.6238*</td><td>1.6650</td><td>1.7648</td><td>1.8393</td></tr><tr><td>SC(n)</td><td>2.4584*</td><td>2.5491</td><td>2.8107</td><td>3.1308</td><td>3.4256</td></tr></tbody></table>

Table 6 PCA-VARI modeling can be interpreted at each location, such as Ŷ̇₁,t representing the input model of the first principal component at the Lembang location. Model interpretation occurs when the values of dew point and humidity that occurred in a month at Lembang climate decrease values by 0.1940. A change in value a month before at Indramayu climate will lead to a 0.3633 increase. When Tasikmalaya climate experiences a change in the previous month, it will increase by 0.1726. Ŷ̇₂,t represents the first principal component of Bogor climate and interprets that a change in the values of dew point and surface root wetness, as most variances occurred a month before at Lembang and Indramayu, leads to an increase by 0.0.2954 and 0.3376. If there is a change in the last month at Tasikmalaya, it will cause an increase of 0.1441. Ŷ̇₃,t indicate the first principal component of the Tasikmalaya. The interpretation model makes the dew point and air temperature different as most variance values occurred in the last months at Bogor climate, thereby increasing the variable value by 0.5371 times this month.
<table><caption>**Table 6:** Parameter estimation of PCA-VARI(1) model</caption><thead><tr><th>Variable</th><th>Y<sub>1,t</sub></th><th>Y<sub>2,t</sub></th><th>Y<sub>3,t</sub></th><th>Y<sub>4,t</sub></th><th>Y<sub>5,t</sub></th></tr></thead><tbody><tr><td>Y<sub>1,t-1</sub></td><td>Φ̂<sup>1</sup><sub>1,1</sub> = -0.1940</td><td>Φ̂<sup>1</sup><sub>2,1</sub> = 0.2954</td><td>Φ̂<sup>1</sup><sub>3,1</sub> = -0.1823</td><td>Φ̂<sup>1</sup><sub>4,1</sub> = 0.2398</td><td>Φ̂<sup>1</sup><sub>5,1</sub> = 0.3802*</td></tr><tr><td>Y<sub>2,t-1</sub></td><td>Φ̂<sup>2</sup><sub>1,1</sub> = -0.5565</td><td>Φ̂<sup>2</sup><sub>2,1</sub> = -0.9009***</td><td>Φ̂<sup>2</sup><sub>3,1</sub> = 0.5371</td><td>Φ̂<sup>2</sup><sub>4,1</sub> = -0.5573*</td><td>Φ̂<sup>2</sup><sub>5,1</sub> = -0.6341*</td></tr><tr><td>Y<sub>3,t-1</sub></td><td>Φ̂<sup>3</sup><sub>1,1</sub> = 0.1726</td><td>Φ̂<sup>3</sup><sub>2,1</sub> = 0.1441</td><td>Φ̂<sup>3</sup><sub>3,1</sub> = -0.6066***</td><td>Φ̂<sup>3</sup><sub>4,1</sub> = 0.1708</td><td>Φ̂<sup>3</sup><sub>5,1</sub> = 0.1898</td></tr><tr><td>Y<sub>4,t-1</sub></td><td>Φ̂<sup>4</sup><sub>1,1</sub> = 0.2018</td><td>Φ̂<sup>4</sup><sub>2,1</sub> = 0.0248</td><td>Φ̂<sup>4</sup><sub>3,1</sub> = -0.3161</td><td>Φ̂<sup>4</sup><sub>4,1</sub> = -0.1910</td><td>Φ̂<sup>4</sup><sub>5,1</sub> = 0.1170</td></tr><tr><td>Y<sub>5,t-1</sub></td><td>Φ̂<sup>5</sup><sub>1,1</sub> = 0.3633*</td><td>Φ̂<sup>5</sup><sub>2,1</sub> = 0.3376*</td><td>Φ̂<sup>5</sup><sub>3,1</sub> = -0.2884</td><td>Φ̂<sup>5</sup><sub>4,1</sub> = 0.2728</td><td>Φ̂<sup>5</sup><sub>5,1</sub> = 0.0454</td></tr></tbody></table>

Note: The mark of ***, **, and * show statistical significance at 0.01, 0.05 and 0.1

Information: Y<sub>1,t</sub> =PC1-LM, Y<sub>2,t</sub> =PC1-BG, Y<sub>3,t</sub> =PC1-TS, Y<sub>4,t</sub> =PC1-SM, Y<sub>5,t</sub> =PC1-IN

<table><caption>**Table 7:** PCA-VARI model estimation coefficient diagnostic test of Granger</caption><thead><tr><th>Variable</th><th>F-Test</th><th>p-value</th></tr></thead><tbody><tr><td>Y<sub>1,t</sub></td><td>1.1064</td><td>0.3021</td></tr><tr><td>Y<sub>2,t</sub></td><td>4.4834</td><td>0.0013</td></tr><tr><td>Y<sub>3,t</sub></td><td>1.8809</td><td>0.0328</td></tr><tr><td>Y<sub>4,t</sub></td><td>1.6996</td><td>0.0411</td></tr><tr><td>Y<sub>5,t</sub></td><td>19.626</td><td>0.0000</td></tr></tbody></table>

<table><caption>**Table 8:** PCA-VARI model estimation coefficient diagnostic test of Ljung-Box</caption><thead><tr><th>Variable</th><th>χ<sup>2</sup></th><th>p-value</th></tr></thead><tbody><tr><td>Y<sub>1,t</sub></td><td>0.1042</td><td>0.7469</td></tr><tr><td>Y<sub>2,t</sub></td><td>7.6877</td><td>0.8090</td></tr><tr><td>Y<sub>3,t</sub></td><td>0.1596</td><td>0.6895</td></tr><tr><td>Y<sub>4,t</sub></td><td>0.2052</td><td>0.6505</td></tr><tr><td>Y<sub>5,t</sub></td><td>2.5374</td><td>0.7708</td></tr></tbody></table>

Ŷ<sub>4,t</sub> represents first principal component of the Sukabumi location, which changes most variance values of the dew point and surface root wetness. The Lembang climate that emerged in previous months caused an increase in the value by 0.2398 times. Ŷ<sub>5,t</sub> As the first principal component of Indramayu, dew point and humidity emerged in the previous month at Tasikmalaya climate, causing an increased variable value of 0.1898.
Table 7 shows the Granger causality test for each first principal component of PCA-VARI model. Variables of $Y_{2,t}$, $Y_{3,t}$, $Y_{4,t}$, $Y_{5,t}$ and Granger against others with *p-value* <0.05 rejected $H_0$ and can be culminated to obtain the diagnostic model test. Meanwhile, $Y_{1,t}$ shows no Granger against others because the *p-value* >0.05, and the diagnostic tests gave a *p-value* > 0.05, which is close to 1 and the significance level. The PCA-VARI model obtained a diagnostic test used to determine the multivariate time series criteria. In Table 8 it can be seen that $\chi^2$ value is close to 1 indicating that it meets the white noise test criteria.

### 3.3 Interpretation and Visualization Model

The PCA-VARI model forecasting estimates between climate locations obtained in this study are represented using the Impulse Response Function (IRF). Its function is to determine the effect of one location's climate on another.

<figure><img src="image_4.png" /><figcaption>**Fig. 3:** Impulse response function (IRF) model PCA-VARI effect of PC1-LM. The x-axis shows the forecast for the month of the next period, and the y-axis shows the forecast standard deviation</figcaption></figure>
Fig. 3 shows the influence of PC1-LM on the other four regions. For instance, its effect on the value index of the Bogor location changes of standard deviation has increased in the first month of January 2021 by 2.1582, as shown in Fig. 3(b). In other words, PC1-BG comprising surface root wetness and humidity decreased to 0.5196 in February 2021 and then fluctuated until May 2021. The same pattern can be seen in Fig. 3(d), namely PC1 Sukabumi, comprising of dew point and surface root wetness, Fig. 3(e) of PC1 Indramayu with dew point and surface root wetness, and Fig. 3(a) PC1-LM Lembang.

<figure><img src="image_5.png" /><figcaption>**Fig. 4:** Impulse response function (IRF) PCA-VARI model effect of PC1-IN (dew point and humidity).</figcaption></figure>

The response by PC1-TS Tasikmalaya (humidity and air temperature) in Fig. 3(c) starts with a decrease of 2.7130 and increases in February 2021 to 0.7205. It decreases to 0.2427 in March and fluctuates until June 2021.

Fig. 4 IRF the effect caused by PC1-IN on PC1-LM, PC1-BG, and PC1-SM. Fig. 4 (a), (b), and (c) have a similar pattern, namely there is no effect in January, with an increase above 0.2000, and a decrease to 0.2000 in February, which fluctuated to the sixth month. Meanwhile, in response to Fig. 4(e) PC1-IN experienced an increase of 0.7959 and 0.03614 in February, with a decrease in March by 0.07694, which varied until June. Significant impact is not seen until the end of the year. For the response to
PC1-TS in Fig. 4(d) in January, there is no response to climate, with a decrease of 0.2295 in February and an increase of 0.15177 until July. Significant impact is not seen until the end of the year.

Fig. 5 shows the IRF effect of PC1-BG on other locations with no response to PC1-LM in the first month, as shown in Fig.5(b). However, it decreased by 0.3277 (dew point and humidity) in February 2021, increased in March by 0.2318, and fluctuated until July 2021, without a response until the end of 2021. The effect on PC1-TS in Fig.5(c) also did not occur at the beginning of the year but increased in February by 0.2392 and decreased by 0.1633 in March, before fluctuating until June 2021. The effect to PC1-SM in Fig.5(d) and PC1-IN in Fig.5(a) seems to have the same pattern, starting with a positive value or increase at the beginning of the year to decreasing in February and increasing again in March. Impulse PC1-BG to PC1-TS in Fig.5(c) has no effect from August to the end of 2021.

<figure><img src="image_6.png" /><figcaption>**Fig. 5:** Impulse response function (IRF) PCA-VARI model effect of PC1-BG</figcaption></figure>

Similarly, the effect of PC1-SM and PC1-TS on the four climates of each location has the same pattern as the area adjacent to the location Bogor. However, there are differences in standard deviations for predictions each month.
# 4 Conclusion

The PCA-VARI model implements a multivariate time series model that reduces the number of observational variables with large data at each climate location through a linear combination of correlated and uncorrelated variables without losing much information. Quantitatively, the relationship between PCA and VARI through the computational process on a multivariate time series plays a significant role in the acquisition of forecasting results. This is common in simplifying the parameter estimation by means of the principal component, which facilitates the visualization and interpretation of the PCA-VARI model. The study analyzes time series data from daily agroclimatology with ten variables for each location. The result is the reduction of climate variables into several principal components. Following the Box-Jenkins rules, comprising of identification, parameter estimation, and model diagnostic testing, the VARI process uses the impulse response function (IRF) to determine the effect between locations of climate variables. Others respond the influence of one region with changes in increasing or decreasing the standard deviation of each climate variable. This is knowledge generated to determine future forecasts for the influence of one region on others. The forecasting results can be concluded that the climate of a location affects those whose coordinates are close together, which is proven using IRF. The influence of climate from one location to another is a recommendation such as regional development that impacts the community [29]. Furthermore, socio-economic activities contribute a positive trend to the analysis of services in improving the economy of a region [30]

# Acknowledgments

The authors are grateful to the Rector of Universitas Padjadjaran, who provided financial support to disseminate research reports under the Academic Leadership Grant year 2022 and Studies Center of Modeling and Computation Faculty of Mathematics and Natural Sciences Universitas Padjadjaran. Gratefully thank the Head of the National Research and Innovation Agency (BRIN), who has supported the funding for the Doctoral Program by Research 2022. The authors are also grateful for the discussion on social media analytics through the RISE_SMA project funded by the European Union from 2019-2024.

# References

1. Kishimoto, R., Shimura, T., Mori, N., Mase, H.: Statistical modeling of global mean wave height considering principal component analysis of sea level pressures and its application to future wave height projection. Hydrological Research Letters, 11(1), 51-57 (2017).

2. Washington, B. J., Seymour, L.: An adapted vector autoregressive expectation maximization imputation algorithm for climate data networks. Wiley Interdisciplinary Reviews: Computational Statistics, 12(6), e1494 (2020).
3. Mal, S., Singh, R. B., Huggel, C., & Grover, A. Introducing linkages between climate change, extreme events, and disaster risk reduction. In Climate change, extreme events and disaster risk reduction (pp. 1-14). Springer, Cham (2018).

4. Pretis, F.: Econometric models of climate systems: The equivalence of two-component energy balance models and cointegrated VARs (2015).

5. Mamipour, S., Yahoo, M., Jalalvandi, S.: An empirical analysis of the relationship between the environment, economy, and society: Results of a PCA-VAR model for Iran. Ecological Indicators, 102, 760-769 (2019).

6. Han, J., Kamber, M., Pei, J.: Data Mining Concepts and Techniques, 3rd edn. Massachu setts: Elsevier Inc, (2012).

7. Niu, J., He, Y., Li, M., Zhang, X., Ran, L., Chao, C., Zhang, B.: A comparative study on application of data mining technique in human shape clustering: Principal component analysis vs. factor analysis. In 2010 5th IEEE Conference on Industrial Electronics and Applications (pp. 2014-2018). IEEE (2010, June).

8. Cerón, W. L., Molina-Carpio, J., Ayes Rivera, I., Andreoli, R. V., Kayano, M. T., Cancha- la, T.: A principal component analysis approach to assess CHIRPS precipitation dataset for the study of climate variability of the La Plata Basin, Southern South America. Natural Hazards, 103(1), 767-783 (2020).

9. Chandra, E., Ajitha, P.: PCA for heterogeneous data sets in a distributed data mining. In Proceedings of the Fourth Annual ACM Bangalore Conference (pp. 1-4) (2011, March).

10. Munandar, D., Ruchjana, B., Abdullah, A.: Principal Component Analysis-Vector Auto- regressive Integrated (PCA-VARI) Model Using Data Mining Approach to Climate Data in The West Java Region. Barekeng: J. II. Mat. & Ter, 16(1), 099-112 (2022).

11. Yu, Y., Wang, D.: Similarity Study of Hydrological Time Series Based on Data Mining. In International conference on Big Data Analytics for Cyber-Physical-Systems (pp. 1049- 1055). Springer, Singapore (2020, December).

12. Du, X., Zhu, F.: A novel principal components analysis (PCA) method for energy absorb- ing structural design enhanced by data mining. Advances in Engineering Software, 127, 17-27 (2019).

13. Snedecor, G. W., and Cochran, W. G.: Statistical Methods. Iowa State University Press (1989).

14. Singh, T., Ghosh, A. and Khandelwal, N.: Dimensional reduction and feature selection: Principal component analysis for data mining. Radiology, vol. 285, no. 3, p. 1055 (2017).

15. Johnson, R. A. and Wichern, D. W.: Applied Multivariate Statistical Analysis, Six edition. Pearson Prentice Hall, New Jersey (2007).

16. Anton, H. and Rorrers, C.: Elementary Linear Algebra, 11th ed. Wiley (2014).

17. Box, G. E. P. and Jenkins, G. M.: Time Series Analysis Forecasting and Control. Holden- Day, Inc (1976).

18. Dickey, D., Fuller, W. A.: Distribution of the estimators for time series regressions with a unit root. Journal of the American Statistical Association, 74(366), 427-431 (1979).

19. Brockwell, P. J. and Davis, R. A.: Introduction to Time Series and Forecasting, 2nd ed. Springer-Verlag, New York (2002).

20. Box, G. E. P. and Cox, D.: An analysis of transformations. J. R. Stat. Soc., vol. B.26, no. 2, pp. 211-252 (1964).

21. Di Asih, I. M., Rahmawati, R.: Vector autoregressive model approach for forecasting out- flow cash in Central Java. In Journal of Physics: Conference Series Vol. 1025, No. 1, p. 012105 (2018, May).

22. Nalita, Y., Rahani, R., Tirayo, E. R., Toharudin, T., Ruchjana, B. N.: Ordinary least square and maximum likelihood estimation of VAR (1) model's parameters and its application
on covid-19 in China 2020. In Journal of Physics: Conference Series Vol. 1722, No. 1, p. 012082 (2021).

23. Granger, C. W. J.: Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, vol. 37, no. 3, pp. 424–438 (1969).

24. Chan, J. C., SHI, J. E.: Application Of Projection-Pursuit Principal Component Analysis Method to Climate Studies. International Journal of Climatology: A Journal of the Royal Meteorological Society, 17(1), 103-113 (1997).

25. Shaharudin, S. M., Ahmad, N., Zainuddin, N. H., Mohamed, N. S.: Identification of rainfall patterns on hydrological simulation using robust principal component analysis. Indonesian Journal of Electrical Engineering and Computer Science, 11(3), 1162-1167 (2018).

26. Shahin, M., Ali, M., Ali, A. B. M.: Vector Autoregression (VAR) modeling and forecasting of temperature, humidity, and cloud coverage. In Computational Intelligence Techniques in Earth and Environmental Sciences (pp. 29-51). Springer, Dordrecht (2014).

27. POWER NASA, https://power.larc.nasa.gov/, last accessed 2022/05/21.

28. WIKIMEDIA, https://upload.wikimedia.org/wikipedia/commons/b/b9/GeoculturalRegionsOfWestJava.svg, last accessed 2022/05/21.

29. Gabriel, A G, P N M Santiago, and R R Casimiro. Mainstreaming Disaster Risk Reduction and Climate Change Adaptation in Comprehensive Development Planning of the Cities in Nueva Ecija in the Philippines. International Journal of Disaster Risk Science 12(3): 367–80. (2021).

30. Newth, D, G Gooley, and D Gunasekera. Socio-Economic Analysis of Climate Services in Disaster Risk Reduction: A Perspective on Pacific SIDS. *Frontiers in Environmental Science* 9 (2021).