STA457

Question 1

Horizontal pattern

Answer 1

Data fluctuates around a constant mean

Question 2

Stationary time series

Answer 2

Statistical properties are independent of time.
The process generating the data has a constant mean.
The variability of the time series is constant over time.
Stationary time series implies horizontal pattern, but not the other way around.

Question 3

Trend pattern

Answer 3

Time series show gradual shifts or movements to relatively higher or lower values over a long period of time.

Question 4

Seasonal pattern

Answer 4

Time series displaying a repeating pattern over a period of time.

Question 5

Trend + seasonal pattern

Answer 5

Time series displaying a repeating pattern over a period of time, while gradually increasing or decreasing over a long period of time.

Question 6

Signal + noise

Answer 6

Signal is deterministic, noise is random

Question 7

Types of white noise

Answer 7

1. Collection of uncorrelated random variables (white noise) with mean 0 and variance \sigma_w^2
2. Collection of noise are independent and identically distributed with mean 0 and variance \sigma_w^2.
3. Gaussian white noise. Collection of noise are iid Normal random variables with mean 0 and variance \sigma_w^2

Question 8

Moving average and filter

Answer 8

Replacing white noise series with moving average (averaging the neighbouring noise).

Question 9

Autoregression

Answer 9

Regression of the current value of the time series as a function of the last value of the series.

Question 10

Random walk with drift

Answer 10

Current value of of time series is a function of the previous value of the time series plus white noise and constant delta, which represents drift

Question 11

Autocovariance function

Answer 11

Covariance of 2 elements of a time series