Lecture 7 - Time Series Analysis A

Question 1

What are the four time series components?

Answer 1

1) Trend
2) Seasonal
3) Cyclical
4) Irregular

Question 2

Define Trend.

Answer 2

Long term upward or downward movements in a given variable over time.

Question 3

Define Seasonal effects.

Answer 3

Repeating patterns or fluctuations over time occurring over a period of less than one year.

Question 4

Define Cyclical effects.

Answer 4

Patterns or fluctuations that occur over periods of more than one year.

Question 5

Define Irregular effects.

Answer 5

Random error and unexplained variations

Question 6

What does smoothing aim to remove?

Answer 6

Irregular effects.

Question 7

What are the two smoothing techniques?

Answer 7

1) Simple Moving Average

2) Exponential Smoothing

Question 8

What is the simple moving average?

Answer 8

The average of n periods either side of the time period. That is, a 3 period moving average is the average of the chosen period, the previous period and the next period.

Question 9

What is the exponential smoothing model?

Answer 9

A weighting, alpha, is chosen between 0 and 1. The forecast for the ‘next’ time period is alpha times the actual value of the current time period plus (1 - alpha) times the forecast value for the current time period.

Question 10

What are the two main disadvantages of a simple moving average?

Answer 10

1) The loss of the first sets of time periods. Key for small data sets.
2) Dropping previous observations makes the model ‘forget’ old data completely.

Question 11

What two measures can be used to review the error of the smoothing models?

Answer 11

MAD and MSE (see formula sheet)

Higher value = more error

Question 12

What is the seasonal index?

Answer 12

A factor that adjusts the trend value of a time series value to compensate for seasonal effects.

Question 13

What model is assumed when constructing a seasonal index with a ratio to moving average?

Answer 13

A multiplicative model whereby:

yt = T x S x C x I

Question 14

What are the 5 steps required to seasonally smooth quarterly data?

Answer 14

1) Compute FOUR period MAs (due to quarterly data)
2) ‘Centre’ the MAs by taking averages of two successive MAs to associate them directly with an observed value
3) Compute the ratio to MA for each time period by dividing the observed value by the centred MA
4) Compute the seasonal indices for each ‘season’ by averaging the ratio to MA for the relevant time period (i.e. combine all march values)
5) Deseasonalise the series by dividing each observation by its relevant seasonal index