Business Forecasting Topic 9

Question 1

non stationary

Answer 1

trend
- ACF dying out extremely slowly -> when data manifests a trend/drift observations tend to be on same side of mean and therefore large autocorrelations still occur at relatively long time lags

Question 2

differencing series to achieve stationarity

Answer 2

differences normally from random series = not constant
sure differences are stationary = model them using one of standard box Jenkins model

Question 3

first difference

Answer 3

differences in sales between successive months
observation lost at start of series

Question 4

random walk model

Answer 4

ARIMA (0,1,0)
first differences of random walk series follow white noise process

Question 5

ACF of random walk model

Answer 5

ACF - indicates non stationarity
take differences = new series is stationary characterised by white noise process -> though strictly such a process requires normal distribution of differences

Question 6

ARIMA (1,1,0)

Answer 6

first differences follow first order autoregressive process
difference between observation for period 2 and 3 is function of difference between periods 1 and 2

Question 7

ARIMA (0,1,1)

Answer 7

first differences followed by a first order moving average model

Question 8

backshift operator (B)

Answer 8

placing in front of observation = has effect of lagging it by 1 period
BY1 = Yt-1

Question 9

over differencing

Answer 9

more differences than required = should avoid
use of first differences in time series analysis = common (sometimes second)

artificially introduce moving average terms into model of differentiated time series = cause unnecessary complications

Question 10

relationship with exponential smoothing models

Answer 10

shown forecasts obtained from exponential smoothing methods are same as those obtained from certain ARIMA models

Simple exponential smoothing forecasts with something constant of α -> ARIMA (0,1,1) forecasts where theta 1 = (1 - α)

holts method = ARIMA (0,2,2)