Seasonality in time series analysis can be defined as recurring patterns and trends in the data over a specific time intervals (such as weekly, monthly, quarterly or yearly). Seasonality plays an important role in forecasting and interpreting the model results. Seasonality factors are taken into account in analyzing sales, stock price data or weather patterns. These patterns, if overlooked, may result into incorrect forecasting and wrongful decisions. For example, a retail store might see a spike in the sales on holiday season. If the seasonality is not taken into account, then the sale forecasting may generate inaccurate results. This is the reason accounting for seasonality becomes important in accurate time series modeling.
To address seasonality, we have the Seasonal Autoregressive Integrated Moving Average (SARIMA) Model available which takes into consideration the seasonal and non-seasonal factors. However, to conduct SARIMA in statistical software like EViews can be challenging and students may make a lot of mistakes that minimizes the accuracy of the forecasting model. This guide will provide a step-by-step tutorial of how to conduct SARIMA modelling using EViews as well as provide examples and recommendations to improve your analysis and forecasting. Further, students can use our EViews assignment help for the reinforcement of the above concept.
What is Seasonal ARIMA Modeling?
The Seasonal ARIMA (SARIMA) model is an extension of the ARIMA model that takes both non-seasonal and seasonal factors into account. While ARIMA models enables capturing trends and autocorrelation in data, SARIMA models also add the seasonality for prediction.
General Form of a SARIMA Model
A SARIMA model is typically expressed as:
SARIMA (p,d,q)×(P,D,Q)s
Where:
- p: Order of non-seasonal autoregression (AR)
- d: Degree of non-seasonal differencing (I)
- q: Order of non-seasonal moving average (MA)
- P: Order of seasonal autoregression (SAR)
- D: Degree of seasonal differencing (SI)
- Q: Order of seasonal moving average (SMA)
- s: Seasonal period (e.g., s = 12 for monthly data with an annual seasonality)
SARIMA models are appropriate for data that shows trend and seasonal pattern, like monthly sales data or quarterly GDP data, which reoccur every year.
Steps for SARIMA Modeling in EViews
Step 1: Plot the Data and Identify Seasonality
The first step in any time series analysis is data visualization in order to inspect for trends and seasonality. Using EViews the data is loaded and the “Graph” function is utilized.
Example: Let us assume that the type of data you are working with is monthly sales. Once you have your data imported into EViews, it is time to generate the plot of the data. In its simplest form, seasonality will be seen if there exists a cycle that recurs after a span of 12 months.
Step 2: Difference the Data to Remove Trends and Seasonality
Before you apply SARIMA, data must be transformed to make it stationary by eliminating the trends and seasonality. In EViews this is done by applying the “Differences” option available in the tool bar.
- Non-seasonal differencing (d): If your data shows an upward or downward movement, apply differencing to remove it.
- Seasonal differencing (D): If your data has a regular seasonal pattern, apply seasonal differencing (e.g., seasonal difference of order 1 for monthly data would subtract the data from 12 months ago).
In EViews, the differenced series can be created by "Genr" command and indicating the orders of seasonal and non-seasonal difference.
Step 3: Identify Model Orders Using ACF and PACF
To identify the appropriate values for p, d, q, P, D, Q, the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots in EViews can be used.
ACF: Helps identify the moving average (MA) and seasonal moving average (SMA) terms.
PACF: Helps identify the autoregressive (AR) and seasonal autoregressive (SAR) terms.
Generate the ACF and PACF plots by selecting View > Correlogram in EViews. Examine these plots to find the lags that are significant for each component.
Step 4: Estimate the SARIMA Model
Once the model orders have been identified, the next step is to estimate the SARIMA model. In EViews, go to Quick > Estimate Equation and specify your model in the following form:
y c ar(1) ma(1) sar(12) sma(12)
In this example:
- ar(1) refers to the non-seasonal AR term.
- ma(1) refers to the non-seasonal MA term.
- sar(12) refers to the seasonal AR term with a lag of 12 periods.
- sma(12) refers to the seasonal MA term with a lag of 12 periods.
EViews will the perform the estimation and display the coefficient estimates, standard errors and a number of other diagnostic statistics.
Step 5: Perform Diagnostic Checks
It is imperative that after estimating the model, diagnostic checks are done to check the goodness of the model fit. In EViews, this involves checking:
- Residual Autocorrelation: Use the Ljung-Box Q-statistic to ensure the residuals are white noise (i.e., no autocorrelation).
- Stationarity: Check for stationarity of data by analyzing the ACF of residuals.
- Model Fit: use metrics like the Akaike Information Criterion (AIC) or Schwarz Bayesian Criterion (SBC) to compare model performance.
Step 6: Forecasting Using the SARIMA Model
When the model has been well-established, one can then predict future values. To do this in the EViews, choose the Forecast and define the period over which the forecast must be made. Any forecast that is generated using EViews will be accompanied with confidence intervals, which can also be plotted and exported.
Common Mistakes Students Make in Seasonality Analysis Using EViews
Some of the challenges that students experience when it comes to analysing seasonality and building the SARIMA models in EViews include the following. Some common mistakes include:
Failing to Test for Seasonality: One thing that many students fail to consider is to check for seasonality in their data. This leads to the cases of developing inaccurate forecasts.
Overfitting the Model: Some students often include many parameters in the SARIMA model in a bid to capture all the minor fluctuations in the data sets which leads to over-fitting. This makes the model too specific with the historical data and minimizes predictability.
Incorrect Identification of SARIMA Components: Differentiating seasonal and non-seasonal components is significant. Students tend to misconceive these factors and this leads to a wrong specification of the model.
Poor Diagnostic Testing: Upon their estimation of the model, students may also ignore other diagnostic checks such as residual analysis for a better model fit. Not checking the residuals for autocorrelation for instance means students are neglecting the chance to fine tune the model to increase precision.
Misunderstanding EViews Output: Eviews computes and displays loads of statistical information. Without deep understanding of these results students may come up with incorrect insights. For example, failing to interpret the results from p-values of coefficients or misunderstanding the Ljung-Box Q-statistic can lead to wrong conclusions.
How EViews Assignment Help Can Resolve These Problems
To resolve such mistakes and have a clear understanding, students must opt for our EViews assignment help that provides detailed step-by-step solution of eviews coursework assignments with comprehensive explanation of results. Our expert guidance can help you:
- Correctly test for presence of seasonality through the use of ACF and PACF.
- Understand the right combination of seasonal and non-seasonal components for SARIMA models.
- To not over-complicate the model by including few relevant parameters in order to minimize over-fitting.
- Interpret the eviews output correctly.
- perform residual diagnostics to check assumptions and make your model more accurate for forecasting.
What You Get with Our EViews Assignment Help
The most on-demand EViews assignment help does not only provide the complete solution of your assignment but also gives you a well-structured and comprehensive report covering all aspects of the analysis. This consists of steps to perform the procedures used in EViews from data import to model estimation and forecasting. You shall also get the EViews work file (.wf1) containing all the command used, the graphs and the output. Moreover, we include annotated screenshots to let you see how we proceeded and the steps applied. We provide insightful interpretations, residual diagnostics and recommendations on model improvement.
Conclusion
Seasonal ARIMA modeling is a powerful tool for analysing time series data with both trends and seasonality. While learning to apply SARIMA in EViews can be challenging, understanding the model's components, performing correct diagnostic checks, and interpreting results accurately are key steps toward success. By avoiding common mistakes and seeking help when needed, students can master this important technique and improve their forecasting abilities.
Are you looking for help with your Time series assignment? Our knowledgeable eviews homework help tutors are available to support you. Learning SARIMA modeling can be made easy. Contact us for guidance and master time series data analysis.
Also Read: How To Correctly Interpret Your Eviews Outputs And Assignment Help Tips
For students searching for textbooks to learn SARIMA modeling, the following texts are recommended:
"Time Series Analysis: Forecasting and Control" by Box, Jenkins, Reinsel, and Ljung – A foundational text on time series modeling, including SARIMA.
"Forecasting, Time Series, and Regression" by Bruce L. Bowerman, Richard T. O'Connell, and Anne Koehler – A comprehensive guide on time series and forecasting methods.
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