Time Series Modeling
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Before we fit any time series model to our data, let's properly create the time variable for the x-axis.

If you haven't created the SALES data set, copy and run the code from the yellow box below:

The time point at each observation is captured in the MONTH, WEEK and DAY columns:

​For example, let's look at the very first observation:

We have:
  • Month = 1
  • Week = 1
  • Day = 4 (Wednesday)

This represents the Wednesday of the first week in the first month.​

We can identify the time point of each observations based on these three columns.

However, in order to perform any type of time series modeling, we need to create a single time column that captures the sequential order of each time point.

One way to create such a column is to convert the DAY, WEEK and MONTH columns into a SAS date column and use it as our x-axis.

Let's look at the very first time point on a calendar.

The sales began to be recorded on the Wednesday of the first week of the month:

This is going to be our initial time point:

Logically, we are going to set this as our timepoint #1.

However, we will set this as timepoint #4 instead.

It really does not matter whether you set this as timepoint #1 or timepoint #4.

We are going to treat this time point as the very first timepoint in this data set.

The timepoint for the next day will be #5. 

The day after will be timepoint #6, and so forth.
​
In month 2, the time point will continue at TP #31:

This will continue until all of the observations in our data set are matched with a unique timepoint on the calendar.

Now, the code to generate the these time points are a little tricky.

Run the code from the box below:
data sales2;
set sales;
cumweek = week + 4*(month-1);
time = day + 7*(cumweek-1);
run;

data day_temp;
do time = 4 to 90;
output;
end;
run;

data sales3;
merge day_temp sales2;
by time;
drop cumweek;
run;

The breakdown of the code will be explained shortly.

​Let's open the SALES3 data set and look at the TIME column that we created:

This is the TIME column that matched what we had on the calendar.

The very first time point is set as 4:

There are four calendar days (i.e. Wednesday, Thursday, Friday, Saturday) in the first week.

These are represented by time point 4 to 7:

Additional rows are also included for the weekends and the holidays. The total sales are set as missing.

Except for the very first week, each week has exactly seven observations:

This matched what we had on our calendar:

This will be the TIME column that we are going to use on our x-axis.

Now, let's look at the breakdown of the code to create this TIME column.

The code contains three data steps.

In the first data step, we created the TIME column:
data sales2;
set sales;
cumweek = week + 4*(month-1);
time = day + 7*(cumweek-1);
run;

The initial value of the TIME column is set as 4. 

This represents Day 4 (Wednesday) in the first week:

On the next day, the TIME value is set as 5. 

The Monday after is set as time point #9.

This reflects what we had on our calendar:

The TIME column matches what we had on our calendar.

However, it is missing the weekends and the holidays:

​The second and third data steps are to fill in the gaps for the weekends and holidays:
data sales2;
set sales;
cumweek = week + 4*(month-1);
time = day + 7*(cumweek-1);
run;

data day_temp;
do time = 4 to 90;
output;
end;
run;

data sales3;
merge day_temp sales2;
by time;
drop cumweek;
run;

The SALES3 data set will have the time point (i.e. TIME column) listed in numerical order matching the dates on our calendar:

In the next section, we will look at the Autoregression plot which is extremely important for time series analysis.
Exercise

A coworker of yours argues that there is a simpler way to create the time column.

She uses each observation as an individual time point.

Below is her code:

data coworker;
set sales;
time = _n_;
run;

The TIME column is shown below:

Each individual observation is treated as a unique time point. 

The time column goes from 1 to 60 for each of the 60 observations.

Is there any issue using this TIME column on our x-axis?

Why and why not?
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