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Words: 1138

## Statistical Modeling and Time Series Analysis Techniques

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### Introduction - Applying Statistical Modeling and ARIMA Techniques to Time Series Data

Statistical modeling is one of the utilization of mathematical models as well as statistical assumptions for producing sample details or building prediction values above real-life world applications. Besides that, a statistic is mainly the probability collection distributions of the possible results for any experiments. In this paper, the induction data analysis process has been described to understand the data visualization part corresponding to the task. Moreover, various types of methods are elaborated in this research paper to execute the program successfully.

### Initial data analysis

Initial data analysis includes various types of execution steps that help the users to perform types of data analysis process accurately. In this section, all the data preprocessing parts are described which helps the user understand the data preparation steps.

Data import is the primary step of the initial data analysis process regarding the task. Moreover, the .csv file has been imported here to execute the task successfully. The read_csv () function has been implemented to import the CSV file within this r studio platform. The dataset file has different types of values, such as numeric, strings, and others that help to create the ARIMA model. Besides that, the view function has been utilized to display the imported dataset file. Furthermore, to display the plots of the entire dataset corresponding to the task.

#### Display the results of the plots

In this case, the plots are displayed after executing the program regarding the task. The plots show the increasing or decreasing values respected with the dataset columns or rows values.

#### Code for the histogram

A histogram displays the frequencies value for the specific dataset values within a range. In this case, the histogram plot has been created by utilizing the above r programming codes corresponding to the task. The plot represents overturining_strength frequencies values that mean it shows the increasing or decreasing rate repeated to the dataset values. Besides that, the str () function has been utilized here to check the internal structure of the imported dataset file. The ggplot library is imported here to display the plots after executing the codes.

#### Calculate the average quarterly means values

The included codes are utilized to create the quarterly values regarding the task. Besides that, the outcome is also shown after executing the represents the average values quarterly.

### Import the metadata and visualized

The metadata and max temp dataset file has been imported here corresponding to the task by utilizing the above R programming codes. The sum (is. na) function has been applied to check the null values available within the dataset file. The view () function has been implemented to display both dataset files in the outcomes area. The plot (drt\$elevation) has been imported here to generate the plots of the elevation values.

#### Methods

In this section, the ARIMA model, as well as the time series model, have been created corresponding to the task. Moreover, the ARIMA is one of the statistical models which utilize the time series data analysis process to predict better future values. This type of method is utilized to realize past details as well as predict future data within a time series. On the other hand, the time series process is one of the specific paths to analyzing the data sequence points stored over the interval time. Besides that, time series forecasting happens while users build specific predictions that mainly depend on historical data.

#### Code for the ARIMA model

In this section, the ARIMA model has been created with the help of a time series analysis process regarding the task. Besides that, the forecast packages have been installed to fit the model. The plot () function is included where year values of the dataset file have been mentioned. The col.main () function has been included that shows the title in the output graph. The auto.arima () function has been utilized to fit the ARIMA model with respect to the year values. The print option is implemented in this program to display the results of the forecast values.

#### Display the graphical representation of the ARIMA model

The above picture shows the graphical form of the ARIMA model that has been created in the above. Besides that, the picture shows the increasing values with the year values of the dataset file.

### Code to fit the time series for the maximum temperature

The above codes are utilized to fit the time series model that predicts the maximum temperature values regarding the task. Moreover, the drt variable is utilized where the read.csv () function has been written to import the metadata.csv file. ggplot () codes are applied to generate the pilots between the longitude as well as latitude values of the metadata file. Besides that, for the time series analysis, the auto.arima () code has been applied. The summary (TM) has been utilized to check the summary of the time series values after executing the task.

#### Results of the times series in the ARIMA model

In this case, the result has been visualized after executing the arima model in this task. Besides that, the coefficient values are also shown in the outcome area. The MAE values, MPE values, and MASE values have been shown in the included figure. The training set accuracy has been visualized after performing the task.

#### Scatter plot between the index value as well as an elevation value

The scatter plot is shown between the index values as well as the elevation values of the dataset file. The pictures represent the increasing as well as decreasing values for the index or elevation values corresponding to the dataset file.

Conclusion

From the above picture, it can be concluded that the time series methods as well as ARIMA models are created corresponding to the task. In the initial data analysis part, the data preparation steps are also visualized to understand the process of the data analysis. Besides that, scatter plotters are created between the index values as well as the elevation values of the metadata file. Besides that, a statistic is mainly the probability collection distributions of the possible results for any experiments. At last, the arima model has been fit for the time series by utilizing the overturning CSV file. The histogram plot has been visualized in this program that represents the frequency values for the overturning_strength values.

References

Khan, F.M. and Gupta, R., 2020. ARIMA and NAR based prediction model for time series analysis of COVID-19 cases in India. Journal of Safety Science and Resilience1(1), pp.12-18.

Satrio, C.B.A., Darmawan, W., Nadia, B.U. and Hanafiah, N., 2021. Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and PROPHET. Procedia Computer Science179, pp.524-532.

Schaffer, A.L., Dobbins, T.A. and Pearson, S.A., 2021. Interrupted time series analysis using autoregressive integrated moving average (ARIMA) models: a guide for evaluating large-scale health interventions. BMC medical research methodology21(1), pp.1-12.

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