# Help Manual

### Contents

• Introduction
• Project
• Analytics Templates
• Change Templates
• Lean Templates
• Graph Templates
• Projects Templates
• Stats Templates
• Analysis
• Miscellaneous

Sigma Magic Help Version 15

# Time Series Analysis

## Application

Time Series Analysis tool can be used to analyze the time series for the given sets of data points. Data has to be collected in a time sequence with an equal interval between data points (for example data collected every hour or data collected every day etc.). This tool can be used to analyze several different facets of the time series data.

This tool can be added to your active workbook by clicking on Stats and then selecting Time Series Analysis.

## Inputs

Click on Analysis Setup to open the menu options for this tool. You can perform four different actions on the time series data: a) analyze the data, b) transform the data, c) smooth the data, and d) forecast new data points. Each of these actions is described below.

### Setup

A sample screenshot of the setup menu is shown below.
1
Data Type: Specify the type of input data. Currently, this analysis is only available for continuous data. Since there is only one option available this textbox has been disabled.
2
X Axis: Specify the type of X-axis you would like for the time series analysis. The available options are:
OptionDescription
IndexIf you specify index, then the subgroups are displayed as 1, 2, 3.
DatesIf you specify dates, then a column will be shown in the Inputs area on the worksheet where you can enter dates for each data point and the subgroups are displayed based on the dates entered.
3a
Time Series Plot: Select this checkbox to create a time series plot of your data. The data is plotted with respect to an index with the first data point at 1, second at 2 and so on...
3b
ACF: Create an auto correlation plot of the data. Auto correlation measures the internal correlation within a time series and varies between -1 and +1. At a lag of 0, the auto correlation value is always 1.
3c
Periodogram: Create a periodogram of the data. The periodogram of the data shows the frequency plot of the data. This plot gives information about how the power or variance in a series is distributed according to the frequency. This plot can be used to detect the periodicity present in the data.
3d
PCF: Create an partial auto correlation plot of the data.
3e
Moving Average: Clicking on this checkbox will create a moving averge smoothing of your data. The moving average is a calculation to analyze data points by creating a series of averages of different subsets of the full data set.

Specify the length to calculate the moving average. For example, if the length is 3, then the first moving average is obtained by averaging the first 3 data points, the second moving average is obtained by averaging 2nd, 3rd, and 4th data point and so on...
3f
Exp Moving Average: Clicking on this checkbox will create an exponential moving average smoothing of your data. The exponential moving average is a type of moving average where greater weight and significance are placed on the most recent data points. The current value of the moving average is calculated as a constant (alpha) times the current value plus (1-alpha) times the previous value of the moving average. Since alpha is less than 1, as you go back in time, the weights keep dropping exponentially.

Specify the value of alpha to use for the exponential moving average. A larger value of alpha give more importance to the most recent points and drops off the older data points much faster from the averaging.
4
Model Selection: Specify the metric to use for the selection of the best model. The available options are:
OptionDescription
MAEUse the Mean Absolute Error. The model with the smallest MAE is the best model.
RMSEUse the Root Mean Square Error. The model with the smallest RMSE is the best model. This is the default setting.
MAPEUse the Mean Absolute Percentage Error. The model with the smallest MAPE is the best model.
5
Help Button: Click on this button to open the help file for this topic.
6
Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
7
OK Button: Click on this button to save all changes and compute the outputs for this analysis.

### Data

If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis.
1
Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and to speed up finding the right data to use for analysis. Enter a few characters in the search field and the software will filter and display the filtered data in the Available Data box.
2
Available Data: The available data box contains the list of data available for analysis. If your workbook does not have any data in tabular format, this box will display "No Data Found". The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is important that you not only specify the column name but also the table name.
3
Add or View Data: Click on this button either to add more data into your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens up the Data Editor dialog box where you can import more data into your workbook, or you can switch from the list view to a table view to see the individual data values for each column.
4
Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, then you will need to select only numeric columns. If the code starts with a T, then you can select both numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data in this box. If the minimum value is 0, then no data is required to be specified for this box.
5
Select Button: Click on this button to select the data for analysis. Any data you select for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to select the data is to double click on the columns in the list of Available Data. Finally, you can also drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
6
Selected Data: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the red color. Note that you can double-click on any of the columns in this box to remove them from the box.

The data you specify for this analysis depends on the options you have specified in the Setup tab.
OptionDescription
1If your X axis variable is specified as Index then the Dates Variable is disabled. Enter the data for which you want to perform the time series analysis under the Analysis Variable.
2If your X axis variable is specified as Dates then you need to specify the column that has dates information under Dates Variable. Enter the data for which you want to perform the time series analysis under the Analysis Variable.
7
View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in a tablular format or in a graphical summary.

### Transform the Data

This tab can be used to re-sample your data to create a new data set. The re-sampling of data allows us to examine the data collected at a different frequency (say monthly instead of daily). The difference operation can be used to remove trends and seasonality in the data. The logarithm of the data can help with the stabilization of variance over time. A sample screenshot of the transform data dialog box is shown below.
 1a None: If you select the None radio button then no transformation is done to your data. 1b Subset: You can use this option to generate a subset of the existing data. This can be used to reduce the total number of data points in your data set. For example, you can sample every 2nd point and save it as another data set. This will reduce your data size by half. Similarly, you can sample every 3rd point and save it to another data set. This will reduce your data size by a factor of a third and so on. This textbox specifies the number of data points for creating the subset of the data. 1c Differences: You can use this option to make a difference with a lag for the given data set. If you select this radio button, we can compute the differences and store the resultant data in another data set. For example, you can do a difference with a lag of 1 so that the data that is stored is Y(2) - Y(1), Y(3) - Y(2), Y(4) - Y(3), etc. Differencing can help stabilize the mean of a time series by removing changes in the level and therefore eliminating or reducing trend and seasonality. Specify the lag that should be used for the differencing operation. A lag of 2 implies the third data point is subtracted from the first data point and so on... 1d Logarithm: You can use this option to take a logarithm of the original data set and save the values to a new data set. The purpose of taking logarithm of a time series is to stabilize the variance of a series. 2 Transform Button: Click on the Transform button to perform the requested transformation for the given data.

### Forecast the Data

You can use this Forecast tab to generate forecasts for your time series data. You can use three different forecasting models: Trends, Seasonality, and Holt-Winter model.
• The Trend model can be used to either model a linear or quadratic trend in the data. If you specify the number of forecasts required, the software will develop the best fit model using regression and then extrapolate the data to the given number of forecasts.
• The Seasonal model will try to remove the seasonality present in the data. You need to specify the seasonal length present in the data.
• Finally, you can also use a Holt-Winter model to generate the forecasts which require three constants.
A sample dialog box for forecasting the data is shown in the figure below.
1
Generate Checkbox: Click and select the Generate Forecasts checkbox in order to generate forecasts.
2
Num Forecasts: Specify the number of forecasts to generate. These forecasts will be generated at the end of the time series.
3
Forecast Model: Specify the type of model to use for generating the forecasts. The available options are:
OptionDescription
TrendGenerate forecasts using a trend analysis of the time series.
SeasonalGenerate forecasts using a sesonal analysis of the time series.
Holt-WinterGenerate forecasts using a Holt-Winter model of the time series.
4
Model Type: Specify the type of model to use for generating the forecasts. For a trend model, the available options are:
OptionDescription
LinearGenerate forecasts using a linear trend.

If you are using a seasonal model or Holt-Winter model, the following options are available:
OptionDescription
AdditiveUse an additive model for forecasting. Additive models are used when the variance of the time series does not change over different periods of time.
MultiplicativeUse a multiplicative model for forecasting. A multiplicative model is typically used if the variance increass with increasing values of the data.

### Charts

If you click on the Charts button, you will see the following dialog box.

### Verify

If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the dialog box is shown in the figure below. The objective of this analysis as well as any checks that are performed is listed in this dialog box. For example, the software may check if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.

## Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. The text output of the analysis contains a summary of the entered data such as minimum value, maximum value, mean, median, etc. Depending on the options selected, the appropriate graphs are added. The different graphs that could be created are the time series plot, auto-correlation plot, partial auto-correlation plot, periodogram, moving average plot, exponential moving average plot, forecasts based on trend, seasonality, and Holt-Winter models.

## Examples

Following examples can be found in the Examples folder.
• Analyze the data given in the reference file (Time Series 1.xlsm).
• Analyze the Los Angeles rainfall data given in the reference file (Time Series 3.xlsm).