PHYSICS 102 Lecture Notes - Lecture 14: Seasonal Lag, Time Series, Business Cycle
Summary Chapter 2 HW – Exploring data patterns with autocorrelation analysis
Data collection
- A forecast can be no more accurate than the data on which it is based
- Four criteria can be applied when determining whether data will be useful:
1) Data should be reliable & accurate
o Reliable source
2) Data should be relevant
o Representative of the circumstances for which they are being used
3) Data should be consistent
o When definitions concerning data collection change, adjustments need to
be made to retain consistency in historical patterns
4) Data should be timely
o Data collected, summarized, and published on a timely basis will be of
greatest value to the forecaster
- Cross-sectional data: observations collected at a single point in time
o Objective: examine such data and extend the revealed relationship to the
larger population
- Time series: data that are collected, recorded, or observed over successive
increments of time (over time)
Exploring time series data patterns
- Four general types of patterns:
1. Horizontal
o When data is collected over time fluctuates around a constant level/
mean → stationary in its mean
2. Trend
o The long-term component that represents the growth/ decline in the time
series over an extended period of time
3. Cyclical
o Wavelike fluctuation around the trend
o Cycles that are not of a fixed period
o Usually affected by general economic conditions (business cycle)
4. Seasonal
o A pattern of change that repeats itself year after year
Exploring data patterns with autocorrelation analysis
- Autocorrelation: correlation between a variable lagged one or more time periods and
itself
- Generally, as the number of
time lags (k) increases, the
magnitudes of the autocorrelation
coefficients decrease
- Correlogram/ autocorrelation function: a graph of the autocorrelations for various
lags of a time series
o Patterns in a correlogram are used to analyse key features of the data
- Autocorrelation coefficients (AC) for different time lags for a variable can be used to
answer the following questions about a time series:
1. Are the data random? – AC are close to zero
o If yes, the autocorrelations for any time lag are close to zero (no relation)
2. Do the data have a trend (are they nonstationary)?
o If yes, successive observations are highly correlated and autocorrelation
coefficients typically are significantly different from zero for the first
several time lags and then gradually drop toward zero as the number of
lags increases
3. Are the data stationary?
4. Are the data seasonal?
o A significant autocorrelation coefficient will occur at the seasonal time lag
or multiples of the seasonal lag (e.g. every January)
o One way to develop seasonal forecasts is to estimate seasonal indexes
from the history of the series
- Autocorrelation coefficients of random data have a sampling distribution that can be
approximated by a normal curve with a mean of zero and an approximate standard
deviation of 1/
- Equation of standard deviation or standard error of autocorrelation coefficients:
(at time lag 1, the standard error 1/ is used)
- At a specified confidence level, a series can be considered random if each of the
calculated autocorrelation coefficients is within the interval about 0 given by
, where the multiplier t is an appropriate percentage point of a t-distribution
Are the Data Random? (1)
- Simple random model: white noise model (
)
