What Is ARIMA Model? And the overview of it

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Apr 06, 2023

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"The ARIMA model is a useful tool for analyzing and forecasting various types of time series data, including financial and economic data, weather data, and traffic data. It is also widely used in industries such as retail, energy, and healthcare for demand forecasting, sales forecasting, and resource allocation. This blog explains the ARIMA model, and by the end of it, you will have a better understanding of ARIMA modelling and the importance of data science training to handle it effectively."

What Is ARIMA Modelling?

If the ARIMA model explained in simple terms, it is a statistical technique used to analyze time series data and make future predictions. It is commonly used to analyze data series such as stock prices, weather measurements, or economic indicators over time. The ARIMA model builds upon the Autoregressive Moving Average (ARMA) technique by considering the transformation of non-stationary time-series data into stationary data that does not show shifts in statistical characteristics over time. This transformation is achieved through a process known as differencing.

The ARIMA model consists of three key components: autoregressive (AR), differencing (I), and moving average (MA). The AR component takes into account the correlation between the current observation and past observations, while the MA component is based on the past prediction error term. By incorporating differencing, the model can achieve stability in data values.

Introduction to ARIMA

Two different methods for time series prediction are proposed: univariate and multivariate. In addition to the series of values, the univariate method uses only the previous values in the time series to predict future values. The multivariate method considers external variables as well to create the forecast.

This model has the capability of predicting a time series based on its past values. It can be applied to any time series that is not random or seasonal and exhibits patterns. In the example of a clothing store, the sales data is a time series since it was collected over a long period of time. One key characteristic of time series data is that it is collected over a regular and consistent period of time. We can modify it according to our needs and use it to predict sales for multiple seasons.

In cases with multiple seasons, the data must be corrected to account for seasonal differences in days because sales change according to the seasons. For instance, holidays fall on different days each year, creating a seasonal effect. The data should be adjusted by the data scientist to obtain an accurate prediction for upcoming sales.

ARIMA is a popular tool for forecasting future demands such as sales forecasts, stock prices, and manufacturing plans. The ARIMA model is becoming increasingly popular among data scientists.

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Autoregressive Integrated Moving Average Model

An autoregressive integrated moving average (ARIMA) model is a widely used time series forecasting method that relies on past observations to predict future values. The model comprises three components: the autoregressive (AR) component, the integrated (I) component, and the moving average (MA) component.

The "AR" component predicts future values based on past values, using a variable that changes according to its own prior values.

"I" - This means that the goal is to achieve stationary data that does not vary with the seasons. This is done by measuring the difference between static data values and previous values. In other words, stationary data have statically constant properties over time, like mean, variance, and auto-correlation. Data scientists determine whether a data series is stationary by using the Augmented Dickey-Fuller (ADF) test.

"MA" - Moving averages are the result of applying a moving average model to previous observations and calculating an observed value based on the residual error.

As a result of the autoregressive part, the time series data is lagged in order to predict the current value of the time series. The order of the autoregressive part is represented by p, which represents the number of lagged values.

The integrated part of the model differentiates the time series so that they become stationary. Stationarity, as a statistical concept, indicates that the means and variance of the series remain constant over time. Differentiating time series to remove seasonality and trends is possible if the series is not stationary. The difference in the integrated part is represented by a "d", which represents the number of differentiations.

Moving averages are calculated by using past errors to predict the current value. The number of past errors used is indicated by “q”, which represents the number of moving averages. 

The ARIMA model is specified using the notation ARIMA(p, d, q) where the parts AR, I, and MA are specified in the order by the integers  "p", "d", and "q".

Maximal likelihood estimation is typically used to estimate the model, and the best model is chosen according to the Akaike information criterion (AIC) or the Bayesian information criterion (BIC).

The ARIMA model can provide useful insight into future trends and patterns in time series data and is widely used in finance, economics, and engineering applications. Several software tools can be used to build ARIMA models, including Python. Data scientists must confirm that the process they are modelling fits the ARIMA model before choosing the model. Using live data and training the model on a dataset, the data scientist constructs and plots a forecast if the dataset is an appropriate fit for the ARIMA model.

Shampoo Sales Dataset

The dataset, collected over a three-year period by data scientist Jason Brownlee, describes sales of shampoo in the United States. There were a total of 36 observations in the dataset. 

To make the dataset stationary, it must go through differencing. Here, the dataset is from actual sales instead of a simplified training set. There may be errors associated with seasonality. 

Data scientists can train their models with training datasets, then generate predictions using test datasets and compare them with training datasets. 

Rolling Forecast ARIMA Model

Rolling forecasts are used to compare time series models. Typically, rolling forecasts are updated every day based on the previous day’s sales data. It is possible to determine if the data series is stationary by plotting the rolling mean and standard deviation, and also to determine if it is not stationary by using the ADF test. When a new data point is collected, a rolling forecast ARIMA model is updated with the new data and generates the forecast for the next time period. 

A rolling forecast ARIMA model is particularly useful for time series data that are non-stationary and may evolve over time. The steps to implement a rolling forecast ARIMA model are as follows:

  1. Load the data: Time series data should be loaded into a Pandas data frame.
  2. Define the training and testing sets: To fit the ARIMA model, split the data into training and testing sets, and then evaluate the model’s performance on the testing set.
  3. Define the ARIMA model: A training set’s autocorrelation and partial autocorrelation plots can be used to determine the order of the ARIMA model.
  4. Fit the ARIMA model: The training set should be fitted with an ARIMA model.
  5. Generate the forecast: Calculate the forecast for the next time step using the fitted ARIMA model. 
  6. Update the model: Fit the ARIMA model on the updated training set after adding the actual value of the next time step and removing the oldest value. 
  7. Repeat steps 5 and 6 for each new time step in the testing set.
  8. Evaluate the model: Evaluation of a model’s performance requires calculating error metrics, such as mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE).

Configuring an ARIMA Model

Experts recommend a dataset with a minimum of 50 observations, preferably 100. This is the first step when applying the ARIMA model to data.

 Here are the other general steps to configure an ARIMA model:

  1. Stationarity Check: You can test the stationarity of the time series by plotting the series, calculating summary statistics, and conducting statistical tests. ARIMA assumes that the data series is stationary, which means that the statistical properties remain the same over time.
  2. Differencing: Using the diff() function in R or the diff() method in Stata will enable you to apply differencing to a time series that is not stationary. The order of differencing (d) determines how many times you need to apply differencing to achieve stationarity.
  3. ACF and PACF Plots: To determine the order of autoregression (p) and moving average (q) after differences, you can use autocorrelation functions (ACFs) or partial autocorrelation functions (PACFs). PACF plots indicate a correlation between lagged values and time series after removing the effects of intermediate lags, whereas ACF plots show a correlation after removing the effects of intermediate lags.
  4. Model Selection: As a result of comparing the ACF and PACF plots, you can identify possible combinations of p and q, and then create several candidate models to evaluate their performance using criteria such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The model with the lowest AIC or BIC value is considered the best model.
  5. Model Validation: When you have chosen the best model, you should evaluate its performance using hold-out data. You can compare the forecasted values with the actual values and calculate evaluation metrics including Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Maximum Amount Percentage Error (MAPE).
  6. Model Refinement: In case the model does not perform satisfactorily, you can refine it with smaller values for p, q, and d, or you can incorporate other variables. In order to choose the optimum model for a particular time series dataset, constructing an ARIMA model generally entails a combination of statistical analysis, visualisation, and experimentation.

Two types of errors are common during the validation or diagnostic stages: overfitting and residual errors. The presence of overfitting indicates that the model is more complex than necessary and that it has been influenced by random noise in the dataset. Having residual errors can alert you to bias in your forecasting model, which may cause inaccurate forecasting.

Merits and demerits of ARIMA model

Merits

  • These are flexible and have the capability to adapt to any wide range of data whether linear or nonlinear rendering the data useful to analyze real-world phenomena.
  • You can use it to predict the future values of time series.
  • These are widely used because of the resources available and considering the fact that it is easy to implement and interpret.
  • The results are also reliable because of the methods used, i.e statistical methods and theory.

Demerits

  • Sometimes the real case scenario may change because the ARIMA model assumes stationary data and for long-term prediction, the accuracy may fall as the forecast horizon increases.
  • ARIMA models' accuracy is limited by the amount of data available, and they can be complex and hard to interpret, especially for non-experts.

Now, all of these concerns can be rectified if the model is handled properly. The Data Science course from StarAgile may be perfect for this task.

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Summary

The ARIMA model is a crucial idea in data science and a potent tool for time series analysis and forecasting. Data scientists can set up an ARIMA model to give important insights into trends, seasonality, and other patterns in time series data by following an organised process of identification, estimation, and validation. Consider enrolling in a StarAgile data science certification course if you're interested in learning more about data science and mastering methods like the ARIMA model. You can develop the abilities and knowledge required to succeed in a data-driven environment by receiving in-depth instruction and practical experience. Not only that, securing Data science certification will help you to get better opportunities than the non certified individuals. Take advantage of this chance to advance your career by enrolling in a StarAgile data science course right away

 

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