# FORECAST.ARIMA

**AXCEL.FORECAST.ARIMA function**

Calculates or predicts a future value based on historical data by using Autoregressive Integrated Moving Average (ARIMA) algorithm. The predicted value is a continuation of historical values. You can use this function to predict sales, revenue, inventory, or consumer trends.

This function requires the data to be organized as a series of data observed at each point of time with a constant step between the different points such as monthly, weekly, or daily.

**Syntax**

AXCEL.FORECAST.ARIMA(data, frequency, start, forecast, [deployment], [plot])

The AXCEL.FORECAST.ARIMA function syntax has the following arguments:

**data** Required. The historical values, for which you want to forecast. You may add external predictors as additional columns. In this case, your external predictor should extend until the end of the forecast horizon. If data has a header, data starts from the second row. Otherwise, the entire vector is considered for the input.

**frequency** Required. Frequency of your data. 365 for daily, 52 for weekly, 12 for monthly, and 4 for quarterly data. If you do not know the frequency, you can set it as 0. In this case, Axcel automatically identifies the frequency of your data.

**start** Required. start date of your data in “yyyy-m-d” format.

** forecast **Required

**. This is the number of periods which we would like to run the forecast.**

**deployment** Optional. You can define a deployment name to deploy your model. After deployment, you can use the deployed function in AXCEL.FORECAST.RUN function. Please note that the deployment name is case sensitive and should include alphabets, numbers, and non-repeating underline. You cannot use underline at the beginning or end of the filename. For instance “abc-123” or “a-b-c-123” are allowed but “abc–123”, “abc-123-“, “-abc-123” or “abc-$123” are not allowed.Depends on your subscription, you can view and restrict access to the deployed model through Axcel web application.

**plot** Optional. default is FALSE. When it is TRUE, Axcel produces the plot inside the sidebar. You can expand the plot and show it in your browser. Please note that no plot is produced when *deployment* is requested. Here is an example of the plot:

when you type *=AXCEL.FORECAST.ARIMA* in an Excel cell, the IntelliSense guides you through required and optional (shows in [] brackets) inputs:

In the example above, we have:

=AXCEL.FORECAST.ARIMA(A1:A145, 12, “2005-03-01”,12,,TRUE)

This means that our data is located at cell A1 through A145, it is monthly, i.e. frequency is 12, it starts from March 1, 2005 (2005-03-01), we would like to forecast for 12 months, we skip the deployment and request for plots. After running this command we have:

Please note that ARIMA function returns dates in Excel format. As a result you may see numbers instead of dates in data_index column. In this case, you need to change the type of column to “Date” from Excel Home menu.

As shown, fitted values and forecasts are reported in the workbook. The first column is the date index, the second column is the actual values used for training of the model, and the next column is the forecast. Axcel also reports the forecast with 80% and 95% confidence to help the process of decision making.

In the console section in the sidebar, model performance, structure, and statistical indicators are reported for validation and transparency in the process. Here is an example:

-------- TIME SERIES Summary --------- Series: y ARIMA(2,1,1)(0,1,0)[12] Coefficients: ar1 ar2 ma1 0.5960 0.2143 -0.9819 s.e. 0.0888 0.0880 0.0292 sigma^2 estimated as 132.3: log likelihood=-504.92 AIC=1017.85 AICc=1018.17 BIC=1029.35 Training set error measures: ME RMSE MAE MPE MAPE MASE ACF1 Training set 1.342299 10.84619 7.86754 0.4206976 2.800458 0.245628 -0.001248475

A template for this function is available here:

### Sales ARIMA Example

See also: *AXCEL.FORECAST.TSLM*, *AXCEL.FORECAST.SPLINE*, *AXCEL.FORECAST.ETS*, *AXCEL.FORECAST.TBATS*