Process or Product Monitoring and Control
6.4. Introduction to Time Series Analysis
|Smoothing data removes random variation and shows trends and cyclic components||
Inherent in the collection of data taken over time is some form
of random variation. There exist methods for reducing of canceling
the effect due to random variation. An often-used technique in
industry is "smoothing". This technique, when properly applied,
reveals more clearly the underlying trend, seasonal and cyclic
There are two distinct groups of smoothing methods
|Taking averages is the simplest way to smooth data||
We will first investigate some averaging methods, such as the
"simple" average of all past data.
Is this a good or bad estimate?
|Mean squared error is a way to judge how good a model is||
We shall compute the "mean squared error":
|MSE results for example||
The results are:
The estimate = 10
|Table of MSE results for example using different estimates||
So how good was the estimator for the amount spent for each supplier?
Let us compare the estimate (10) with the following estimates: 7,
9, and 12. That is, we estimate that each supplier will spend $7,
or $9 or $12.
Performing the same calculations we arrive at:
The estimator with the smallest MSE is the best. It can be shown mathematically that the estimator that minimizes the MSE for a set of random data is the mean.
|Table showing squared error for the mean for sample data||
Next we will examine the mean to see how well it predicts net income
The next table gives the income before taxes of a PC manufacturer between 1985 and 1994.
The MSE = 1.9508.
|The mean is not a good estimator when there are trends||
The question arises: can we use the mean to forecast income
if we suspect a trend? A look at the graph below shows clearly
that we should not do this.
|Average weighs all past observations equally||
In summary, we state that