STA3041F Test 2 Definitions

Main Objectives of Time Series Analysis

Description, modelling, forecasting, control

Description

The salient features of a series are described by using summary statistics and/or graphical illustrations.

Modelling

Modelling of several variables may be undertaken to quantify the relationship between them.

Forecasting

particularly important in the investment community for evaluating the best strategies. Based on the premise that the statistical model that best represent a data set will continue to be valid in the short term.

Control

Time series models may be developed in order to study the complex dynamics.

Trend

A series that exhibits a long-run growth or decline (at least over successive time periods) is said to be a trending series.

Seasonal Variation

Present in a data set when similar patterns in a data set are observed at similar times during the year.

Cycles

Recurring up and down movements around any trend line of a series. May vary in length and difficult to model if the time series is short.

Noise or Random Fluctuation

Represents the variation that remains after one assigns the trend, seasonal and cyclical components of a time series.

Stochastic Process

A mathematical description of a distribution of a time series. used as a model to generate time series.

Time Series

A sequence of observations ordered in time

∇

Differencing operator: Can directly remove the trend.

Linear Filter

Transforms a time series y1, y2 ... , yn to y^~1 etc using the linear operation where wr is a set of weights that sum to one.

Independent Increment

A counting process has independet increments if the numbers of events that occur in non-overlapping (disjoint) time intervals are indepent

Stationary Increment

A counting process has stationary increments if the distribution of the number of events that occur in any interval of time depends only on the length of the time interval.

Stationary Time Series

One whose properties do not depend on the time at which the series is observed - will have no predictable patters in the long term

Reasons for Transformation

To stabilise the variance, make the seasonal effect additive and make the data normally distributed.

Weak Stationarity of Order 1

When a stochastic process only has constant mean

Weak Stationarity of Order 2

When a stochastic process has a constant mean and the covariance structure only depends on the lags k.

Correlogram

A plot of all the lagged autocorrelations against lags k