# Time Series

**Topics:**Time series analysis, Time series, Moving average

**Pages:**8 (2280 words)

**Published:**March 3, 2012

Introduction

Economic and business time series analysis is a major field of research and application. This analysis method has been used for economic forecasting, sales forecasting, stock market analysis and company internal control. In this paper, we will talk about time series and review techniques that are useful for analyzing time series data. Definition of Time Series and Time Series Analysis

Time series is an ordered sequence of values of a variable at equally spaced time intervals. Time series data often arise when monitoring industrial processes or tracking corporate business metrics. The analysis of time series is based on two basic assumptions. One is successive values in the data file represent consecutive measurements taken at equally spaced time intervals. The other assumption is that time is the only one independent variable in time series function. Applications of Time Series Models

•Identify the nature of the phenomenon represented by the sequence of observations, and •Fit a model and proceed to forecasting, monitoring or even feedback and feedforward control. Both of these goals require that the pattern of observed time series data is identified and described. Once the pattern is established, we can interpret and integrate it with other data and use the identified pattern to predict future events.

Decomposition Analysis of Time Series

In order to identify patterns that appear simultaneously in a time series, we use decomposition analysis to separate and decompose different influences or components out of the ‘raw’ data,. In general, there are four types of components in time series analysis: trend, seasonal variation, cyclical variation and irregular variation. Thus, the value of the time series Y can be represented by the following equations: Yt = Tt * St* Ct *It or Yt = Tt +St +Ct +It Where Yt = Actual value of the data in the time series at time t Tt = Trend value at time t

St = Seasonal variation at time t

Ct = Cyclical variation at time t

Rt = Random variation at time t

Depending on the kind of time series being calculated, the formula might be additive or multiplicative. •Trend

A trend is a relatively smooth long-term movement of a time series. It is the first basic element that affects data collection in time series analysis. It can be described as the growth or decay tendencies for data to increase or decrease fairly steadily over a period of time. Long-term trend is typically modeled as a linear, quadratic and exponential function. •Seasonal Variation

When a repetitive pattern is observed over some time horizon, the series is said to have seasonal behavior. It is usually associated with calendar or climatic changes and is frequently tied to a yearly cycle, which regularly fluctuates and repeats yearly about the same time and level of intensity. •Cyclical Variation

Cyclical variation is an upturn or downturn not tied to seasonal variation but usually results from changes in the overall economic conditions such as recession and expansion. •Irregular Component

The first three components are deterministic which are called “Signals”, while the irregular component is a random variable, which can be described as any fluctuation not classified as one of the previous elements. It is unexplainable therefore it is unpredictable. Decomposition Procedure

To be able to make a proper forecast, we must know to what extent each of the above components is present in the data. Hence, to understand and measure these components, the forecast procedure involves initially removing the component effects from the data (decomposition). After the effects are measured, making a forecast involves putting back the components on forecast estimates (recomposition). The time series decomposition process is depicted by the following flowchart:

The first step of a time series decomposition is to identify and...

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