Business Forecasting Topic 8

Question 1

Box Jenkins

Answer 1

ST forecasting
- exploit correlation between observations at different points in time

1. identify tentative model
2. use series of diagnostic tests to assess model adequacy

Question 2

stationarity (time series)

Answer 2

structure doenst change over time

each distribution = same mean and variance irrespective of time period

mean and variance = constant over whole time span of series

Question 3

autocorrelation

Answer 3

correlation of a variable with itself at different times
-graphed above confidence limit = significant -> confidence limit requires std dev and mean

Question 4

partial autocorrelation

Answer 4

how much of a correlation is there between sales k-periods apart, when the effects of the intervening weeks are removed

pattern of PACFs = help us identify forecasting model appropriate for given time series

above confidence limit = significant
influence of intermediary things are removed

Question 5

significance tests

Answer 5

applied to ACF and PACF based on null hypothesis that data is completely random

approx standard error = 1/ root of n (n = number of data points)

Question 6

calculating the ACF or PACF coefficients

Answer 6

significant values lie outside

these values are plotted as confidence limits on the diagrams

Question 7

autoregressive models

Answer 7

first order autoregressive model

Question 8

ACF AND PACF for autoregressive models

Answer 8

ACF - declines rapidly to zero (exponentially) or oscillates between positive and negative values and dying

PACF- cuts off after lag 1

Question 9

moving average models

Answer 9

• show relationship between variable to be forecast shocks in earlier periods

Question 10

ACF AND PACF for moving average models

Answer 10

exact reverse of first order autoregressive

Question 11

mixed models

Answer 11

• involve both autoregressive and moving average terms

Question 12

ACF AND PACF for mixed models

Answer 12

both decline rapidly to zero

Question 13

ARIMA

Answer 13

• classify different models that are available
  ARIMA (p, d, q)

ARIMA (1,0,0) = first order autoregressive
ARIMA (0,0,2) = second order moving average
ARIMA (1,0,1) = mixed model

Question 14

degree of differencing

Answer 14

stationary series require no differencing

Question 15

stages in box Jenkins approach to forecasting

Answer 15

1. identify appropriate model
2. estimate model parameters
3. use diagnostic tests to make sure these parameters are appropriate
4. use model to make forecasts

Question 16

series of 4 diagnostic checks to test adequacy

Answer 16

1. are residuals of model white noise
2. residuals approximately normally distributed
3. coefficient in model significantly different from zero
4. overfitting

Question 17

residuals white noise

Answer 17

residual = actual sales = model prediction

not white noise = still some pattern in series that model isn’t picking up (pattern useful for forecast)

below confidence limit = white noise

Question 18

residuals approx normally distributed

Answer 18

assumption necessary for t test

Question 19

coefficient in model significantly different from zero

Answer 19

if not = suggest constant is 0 and or previous sales provide no useful info for this week

p value below 0.05 - significantly different from zero

Question 20

overfitting

Answer 20

fitting series of more complex models to data and seeing if coefficients for extra terms are sig different from zero

p value > 0.05 = coefficient is not sig diff from zero - indicates original model probs adequate for time series

Question 21

making forecasts

Answer 21

• forecasts can be expressed in form of confidence intervals
• forecasting from ARIMA (0,0,1) = more problems need to know error (shock) in forecasting final figures