# FORECAST.TSLM

**AXCEL.FORECAST.TSLM function**

Calculates or predicts a future value based on historical data by fitting A Linear Model With Time Series Components including trend and seasonality components. The main advantage of this model is its simple approach which is a linear regression with additional terms of trend and seasonality. 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.TSLM(data, frequency, start, forecast, [deployment], [plot])

The AXCEL.FORECAST.TSLM 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-mm-dd” 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. Depending on your subscription, you can view and restrict access to the deployed model through the 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*.*TSLM* in an Excel cell, the IntelliSense guides you through required and optional (shown in [] brackets) inputs:

In the example above, we have:

=AXCEL.FORECAST.TSLM(B1:C350, 12, “1992-1-1”,6,,TRUE)

This means that our data is located at cell B1 through C350, it is monthly, i.e. frequency is 12, it starts from January 1, 1992 (1992-01-01), we would like to forecast for 6 months, we skip the deployment and request for plots. After running this command we have:

Please note that TSLM 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 --------- Call: tslm(formula = equation) Residuals: Min 1Q Median 3Q Max -1682.2 -683.3 -275.4 461.7 3010.4 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6888.3798 282.0309 24.424 < 2e-16 *** Unemployment -387.1169 32.9233 -11.758 < 2e-16 *** season2 -216.3344 262.4223 -0.824 0.41033 season3 1337.2375 262.4142 5.096 5.92e-07 *** season4 714.1357 262.4095 2.721 0.00685 ** season5 1440.3250 262.4044 5.489 8.19e-08 *** season6 897.0797 262.4055 3.419 0.00071 *** season7 1155.5699 262.4033 4.404 1.45e-05 *** season8 1213.8513 262.4019 4.626 5.40e-06 *** season9 -92.9539 262.4048 -0.354 0.72339 season10 413.8069 262.4101 1.577 0.11579 season11 -230.2235 262.4149 -0.877 0.38096 season12 1187.5064 262.4215 4.525 8.49e-06 *** trend 59.6121 0.5549 107.432 < 2e-16 *** --- Signif. codes: 0 "***" 0.001 "**" 0.01 "*" 0.05 "." 0.1 " " 1 Residual standard error: 990.4 on 323 degrees of freedom Multiple R-squared: 0.9735, Adjusted R-squared: 0.9724 F-statistic: 911.3 on 13 and 323 DF, p-value: < 2.2e-16

A template for this function is available here:

### Sales TSLM Example

See also: *AXCEL.FORECAST.ETS, AXCEL.FORECAST.SPLINE, AXCEL.FORECAST.ARIMA, AXCEL.FORECAST.TBATS, and AXCEL.FORECAST.RUN*