The Complete Guide to Time Series Models

Introduction
Time series analysis is a statistical technique which is used for analyzing and predicting the data that evolves over time.it has applications in different fields like economic, finance, forecasting. time series models are mathematical models which capture the patterns and relationships within the time-independent data. In this article we provide a complete guide for understanding and implementing time series models.
What is time series?
Time series is a set of points which are collected at regular intervals over time. we can represent them as a set of observant shown over the time. time series data often shows trends, seasonality, and other patterns that can be analyzed and utilized for forecasting future values. The main goal in using a time series is to predict future values. The first step in time series is to draw a graph of the data. with drawing a graph, we can identify general information, including an upward or downward trend, the presence of a seasonal pattern, a periodic trend, and the presence of outliers in the data. After plotting the data, the data must be stationary in order to have a proper prediction. Data can be made static by using differentiation or decomposition into its constituent components. After stabilizing the data, the order of the moving average and the order of autoregression of the model can be identified using the graph. It is necessary to examine the obtained parameters for significance using T-test. If it is significant and there is no dependence in the remainder, a suitable prediction can be made with the help of past data, also the predicted values can be evaluated using the absolute average percentage of error.
The component of time series models
Time series models are consist of 3 part:
• Trends: long term pattern or movement in data.
• Seasonality: predictable or repetitive patterns that happen in a specific time period.
• Residuals: The random fluctuations or noise in the data that we cannot explain them by the trend or seasonality.
Different kinds of time series models
• Autoregressive Integrated Moving Average (ARIMA)
• Exponential Smoothing (ES)
• Seasonal Autoregressive Integrated Moving Average (SARIMA)
• Vector Autoregression (VAR)
Analyzing and choosing model
For choosing the best time series model for a specific dataset, we can use different evaluating techniques. These include analyzing residual plots, calculating evaluation metrics like mean squared error (MSE) or Akaike Information Criterion (AIC), and performing cross-validation.
Model Training and Forecasting
When we choosed the appropriate time series model we have to train the model with historical data. This happens with estimating the model parameters based on the data. we can use the model to predict future values by extrapolating the patterns captured in the training phase.