Module 1: Forecasting Flashcards
What is forecasting?
Why are we interested?
What is forecasting?
Primary function is to predict
the future
Why are we interested?
Affects the decisions we
make today
What are the characteristics of forecasts?
They are usually wrong
A good forecast is more than a single number and includes some
measure of error
- Variance
- Range
Aggregate forecasts are usually more accurate
Accuracy erodes as we go further into the future
The method should be easy to use and understand in most cases
What are some subjective forecasting methods?
Sales Force Composites
Aggregation of sales personnel estimates
Customer Surveys
Jury of Executive Opinion
The Delphi Method
- Individual opinions are compiled and reconsidered. Repeat until
and overall group consensus is (hopefully) reached.
No historical data available (e.g. new product)
What are the 2 objective forecasting methods?
Two primary methods: causal models and time series methods
Causal models:
Let Y be the quantity to be forecasted and (X1, X2, . . . , Xn) be n
variables that have predictive power for Y. A causal model is
Y = f(X1, X2, . . . , Xn).
A typical relationship is a linear one. That is,
Y = α0 + α1X1 + · · · + αnXn
Time Series Methods: A time series is just a collection of past
values of the variable being predicted. Also known as naive
methods. Try to isolate patterns in past data.
- Trend
- Seasonality
- Cycles
- Randomness
What is the notation of time series models?
Let D1, D2, . . . , Dt, . . . be the past observed values of demand in
periods 1, 2, . . . , t, . . . , respectively
If we are making a forecast in period t (for period t
0 > t), we will assume we have observed D1, D2, . . . , Dt but not Dt+1
Let Ft,t+τ be the forecast made in period t for the demand in
period t + τ where τ = 1, 2, 3, . . .
Then Ft−1,t is the forecast made in t − 1 for t and Ft,t+1 is the
forecast made in t for t + 1 (one-step-ahead). We use shorthand
notation Ft = Ft−1,t
We denote e_t the forecast error in period t. It is the difference
between the forecast for demand in period t and the actual value
of demand in t
- For a multiple step ahead forecast: et = Ft−τ,t − Dt
- For one step ahead forecast: et = Ft − Dt
What is the bias in forecasts?
A bias occurs when the average value of a forecast error tends to
be positive or negative.
Mathematically an unbiased forecast is one in which sum of i=0 till infinity e_i=0
What is a stationary time series?
A stationary time series has the form:
Dt = µ + epsilon_t , ∀t ≥ 1,
where µ is an unknown constant corresponding to the mean, and
epsilon_t is a random error with mean 0 and variance σ^2
What are the two common methods for forecasting stationary series?
Two common methods for forecasting stationary series are
moving averages and exponential smoothing.
What is moving averages?
see docs
MA is a method for forecasting stationary demand. Hence, the
forecast made in period 3 for any future period will be the same.
Although the on-step-ahead forecast will be more accurate.
What are the advantages and disadvantages of MA?
Advantages of Moving Average Method
- Easily understood
- Easily computed
- Provides stable forecasts
Disadvantages of Moving Average Method
- Requires saving all past n data points
- Lags behind a trend
What is exponential smoothing?
see docs
What are the similarities and differences between ES and MA?
Similarities:
- Both methods are appropriate for stationary series
- Both methods depend on a single parameter
- Both methods lag behind a trend
- One can achieve the same distribution of forecast error by setting
α =2 / (n+1) ⇒ See Exercise 5 from TL1
Differences:
- ES carries all past history. MA eliminates “bad” data after n periods
- MA requires all n past data points while ES only requires last
forecast and last observation.
Which measures to use to evaluate the forecasts made?
see docs
What is Holt’s method for ES>
see docs
What is the procedure of Holt’s method for exoponential smoothing?
see docs
