Question

2. If a quarterly time series has additive seasonality, then find out the missing value

Answer 1

Answer:

Up until now we assumed our time series is generated by a stationary

process - either a white noise, an autoregressive, a moving-average or an

ARMA process.

However, this is not usually the case with real-world data - they are often

governed by a (deterministic) trend and they might have (deterministic)

cyclical or seasonal components in addition to the irregular/remainder

(stationary process) component:

I Trend component - a long-term increase or decrease in the data

which might not be linear. Sometimes the trend might change

direction as time increases.

I Cyclical component - exists when data exhibit rises and falls that

are not of fixed period. The average length of cycles is longer than

the length of a seasonal pattern. In practice, the trend component is

assumed to include also the cyclical component. Sometimes the

trend and cyclical components together are called as trend-cycle.

I Seasonal component - exists when a series exhibits regular

fluctuations based on the season (e.g. every month/quarter/year).

Seasonality is always of a fixed and known period.

I Irregular component - a stationary process.Step-by-step explanation: