1. TOPIC VI. FORECASTING
BASED ON EXPONENTIAL
SMOOTHING
Content
1. Exponential smoothing method
2. Double exponential smoothing method
2. Exponential smoothing method
Exponential smoothing is popular
technique for short-run forecasting by
business forecasters.
This method is commonly applied to
financial market and economic data, but it
can be used with any discrete set of
repeated measurements.
3. Financial market includes:
1. Capital market is a market for securities (debt or
equity), where business enterprises, companies and
governments can raise long-term funds. It includes the
stock market (equity securities) and the bond market
(debt).
Stock market or equity market is a part of the capital
market for the trading of company stocks (shares) at an
agreed price. Items that can be forecasted are the
common stock price and preferred stock price.
Bond market is a financial market where participants buy
and sell debt securities, usually in the form of bonds.
Bond price is an item that can be predicted.
4. Financial market types:
2. Foreign exchange market (or currency
market) is a component of the financial market for the
trading of currencies. The foreign exchange market
determines the relative values of different currencies.
The foreign exchange market can assist trade and
investment, by allowing businesses to convert one
currency to another currency. The foreign exchange
market is the largest and most liquid financial market
in the world.
Items that can be forecasted are the exchange rate
and investments.
5. Financial market types:
3. Insurance market is a financial market that
facilitates the redistribution of various risks.
Insurance is a form of risk management
primarily used to hedge against the risks,
uncertain losses. Insurance is defined as the
equitable transfer of the risk of a loss, from one
entity to another, in exchange for payment. An
insurer is a company selling the insurance.
Items that can be forecasted are the insurance
premium, insurance tariff, redemption value,
etc.
6. Financial market types:
4. Credit market (or money market) is a
component of the financial market for
assets involved in long-term and short-term
borrowing and lending. Credit is the
movement of borrowed capital between
economic entities. Credits are the funds
provided to economic entities by banks
and other financial institutions in the form
of investment, trade credits and loans in
order to obtain the percent.
7. Exponential smoothing method:
theoretical material
Exponential smoothing is forecasting technique that can
be applied to time series, either to produce smoothed
data to make forecasts. This method assigns
exponentially decreasing weights as the observation
get older. The procedure gives heaviest weight to more
recent information and smaller weights to observations
in the more distant past. The reason for this is that the
future is more dependent upon the recent past than on
the distant past.
So, exponential smoothing weights past observations with
exponentially decreasing weights to forecast future
values. In the exponential smoothing the most recent
observations have the greatest influence to forecast.
9. Example 1: a company must develop forecast for the next month. It has
collected data on price per common share for the past 10 months (table
1). Find the forecast of price per common share for February using simple
exponential smoothing, if the smoothing factor a is 0,3.
10. Forecast accuracy measurement
Absolute forecast error (AFE) is the
difference between actual statistical data
and forecast values.
Mean forecast error (MFE) is a quantity
used to measure how close forecasts are
to the eventual outcomes. It is
calculated by adding all absolute
forecast errors and then dividing this
total by the number of periods (n).
13. Double exponential smoothing
Double exponential smoothing is a refinement of the simple
exponential smoothing model but adds another component
which takes into account any trend in the data. Simple
exponential smoothing models work best with data where
there are no trend or seasonality components to the data.
When the data reflects either an increasing or decreasing
trend over time, simple exponential smoothing forecasts tend
to lag behind observations.
Double exponential smoothing is designed to address this type
of data series by taking into account any trend in the data. As
with simple exponential smoothing, in double exponential
smoothing models past observations are given exponentially
smaller weights as the observations get older. In other words,
recent observations are given relatively more weight in
forecasting than the older observations.
14. Forecast calculation with double
exponential smoothing:
1 step: Find the forecast based on simple
exponential smoothing method by the
formula:
1 1 ˆ (1 ) ˆ - - = × + - × ES t t у a y a y
16. Forecast calculation with double
exponential smoothing:
3 step: Find the forecast based on double
exponential smoothing method.
Forecast based on double exponential
smoothing is calculated by adding the
forecast based on simple exponential
smoothing and best estimate of the trend for
the time period t.
^
DES ES t y = yˆ + b
17. Example 2: using above example we need to compute the forecast
of price per common share for February using double exponential
smoothing, if the trend smoothing factor is β=0,2.
