Introduction

defined as a set of quantitative observations zt arranged in chronological order

set of times at which observations are made is a discrete set

• e.g.; observations are made at fixed time intervals

are obtained when observations are recorded continuously over some time interval

Measure data will include the random component

• therefore, the data of the time series is considered as the realization of random variables

Systematic change in the mean level of time series that does not appear to be periodic

Data show repeating pattern within each year

(quit long) time periods, for which values decrease

• cross-sectional data

• time seires data

• pooled data

• type of data collected by observing many subjects at the same point of time, or without regard to difference in time

Pooled data combines both cross-sectional data and time series data

• panel data differs from pooled cross-sectional data

• differs from pooled cross-sectional data, because it deals with the observations on the same subjects in different times whereas the latter observes differnet subjects in different time periods

• using panel data, we can studdy how the subjects change over time

• time series data have a natural temporal ordering

• case of time series: observations are generally not independent across time

  • often strongly related to their recent histories

• time series values corresponding to different time points usually do not have the same distribution

• data frewuwncy at which data are collected:

  • daily

  • weekly

  • monthly

  • quarterly

  • annually

• exploratory analysis

• forecasting

• process control

• time series regression

• identifying the nature of the phenomenon represented by the sequence of observations

• mainly involves visualization with time series plots, decomposition of the series into deterministic and stochastic parts, and studying the dependence structure in the data

• predicting future values of the time series variable

• relies on extrapolation, and is generally based on the assumption that past and present characteristics of the seires continue

• it seems obvious that good forecasting results require a very good comprehension of a series’ properties, be it in a more descriptive sense, or in the sense of a fitted model

Man production or other processes are measured quantitatively for the prupose of optimmal managment and quality control

• fit stochastic model, which allows understanding the signal in the data, but also the noise

• using the model, it is feasible to monitior which fluctuations in the production are normal, and which ones require intervention

Understand the relation between a so-identified response time series, and one or more explanatory series

• number of methods have been introduces by practioners to solve these tasks (goals)

• understand method as the calculation rule

• methods are mostly based on common sense and intuiotn

• question is about the reliability of thee methods

• methods used should be based on mathematical models of time series

• model is a mathematical description of how randomness affects the generation of data in the rime series

• based on the model, it is possible to verify its suitability for describing a particular time series and derive theoretically reasoned calculation rules for forecasting the future and for finding confidence limits for forecast

• theory of time series consists in describing the models and derivation of their properties

• choice of a suitable mathematical model

• model calibration (matching) with existing data (model parameter estimation), model goodness of fit check

• use of calibrated model forecastinf, finding variation of the forecasting errors and confidence limits for forecasts