SUMMARY
EXPONENTIAL: Each time series is modeled using an exponential curve, also called a geometric curve.
Equation:
Yt = k + aebt
, where Yt is the value of the time series at time t, and a, b, and k are estimated from the data using least-squares estimation.
(The value k allows the exponential curve to shift to better fit the time series.)
The application, futurera, uses a modified exponential.
Yt = a - b(rt)
where, a, b and r are
positive constants, r is less than 1 and t=1 for year 1.
An example serie is in the Examples Data as General curve.
Instead the original data, we could smooth it with a moving average and use it for the slopes and trend calculations. See some summary charts at the end of the page.
From the table from introduction:
For a simple modified exponential trend curve the demand increases by a constant proportion each year, and the ratio of the of the demand to the demand itself is constant.
We think that a exponential trend is the right solution. We should then check with the log slopes. If we find a trend sloping down to the right then that is the modified exponential trend we are looking for.
We are looking for a trend that is sloping down to the right. We will chhose a line.
This is calculated with Trend, then the Line option in the application.
Parameters: start year (2010) and end year (2019).
One that the application suggest is shown in next graph.
This is calculated with Trend, then the Modified exponential option in the application.
Parameters: start year (2010) and end year (2021). And set the serie with two decimals.
Equation where X is the exponential trend line.
Yt = 123.36 - 102.33 * (0.93t)
The exponential curve type is useful for data that rapidly increases or decreases with time.
Demand serie is in the Examples Data as General curve.
From Demand we make series with moving averages length 3 and 5. These moving averages we take the Trend with modified exponential.