An important way that we can use models is to plan for the future.
This is obviously important from a work perspective, as our ability to model what is going to
happen in the future, and it be relatively accurate, is important
We must remember the process to do this is quite difficult as we have to deal with historical
data over time.
This historical data on a single variable is called time series .
The procedure to do forecasting is called time series methods.
Forecasting methods can be quantitative or qualitative. For the purposes of this course we
are obviously interested in quantitative.
The quantitative methods we will look at can be studied when:
(1) past information about the variable being forecast is available.
(2) the information can be quantified.
(3) there is a reasonable assumption that the patterns in the past will predict the future
Components of a Time Series
The gradual shifting of a time series is referred to as a trend .
Trends can be linear, nonlinear, or simply have no trend at all.
Below is an overview of all the different forecasting methods
that will soon be available to you:
Trend lines will tend to show groups of points that cycle above and below the
Any recurring sequence of point above or below the trend line lasting more than
a year can be attributed to the cyclical component of the time series.
For example: A boom or bust cycle in the economy will cause market indices
to be below normal for an elongated period of time. Shown below, the S&P
Trends can also have seasonal, or simply irregular components.
Moving averages, weighted averages, and exponential
smoothing are three types of smoothing methods.
The objective of each of the methods is to smooth out random
fluctuations caused by irregular components of the time series.
Smoothing methods are appropriate for stable time series
-That is, ones that do not exhibit significant cyclical effects such
They do not work well when these types of cyclical effects are
In particular exponential smoothing is good for large numbers
Uses the most recent n data points in the time series as the
forecast for the next period.
Moving Average = Σ(most recent data values)/n
The term moving is used because every time a new data point
becomes available is replaces the oldest one.
Weighted Moving Average
Involves finding a different weight for each data value and
multiplying each point by that value in the moving average
Obviously, this is useful for when we are not dealing with too
many data points.
Weighted Average = (w1*p1 + w2*p2 + ...+ wn*pn)/n
In practice, forecast Accuracy is a big issue here as assigning
the values to use and weights to them requires in-depth
knowledge of what you are trying to forecast.
Uses a weighted average of past time series values as the forecast.
Special case of the weighted moving average as we select only one weight--the weight for
the most recent observation.
The weights for the other values are computed automatically and become smaller as the
observations move farther in to the past.
Ft+1 = αYt + (1 - α)Ft where:
Ft+1 = forecast for the time series period for t+1.
Yt = actual value of the time series in period t
Ft = forecast of the time series for period t.
α = smoothing constant (0 ≤ α ≤ 1).
Recall, in Simple Linear Regression: ŷ = b0 + b1x
In forecasting the independent variable is time.
To emphasize this we re-write the equation above as follows:
Tt = b0 + b1t, where
Tt = trend value of the time series in period t.
b0 = intercept of the trend line.
b1 = slope of the trend line.
t = time (lower t's correspond to the oldest time series value)
Also similar to SLR is how we compute b0 and b1.
For these equations, refer to Figures 18.6 and 18.7 in the book.
End of Chapter 18 Part I
Let me know if you have any questions.
Please read the chapter.
Please do your homework.