Time series data affect many aspects of our lives. This paper highlights ten things we should all know about time series, namely: a good working knowledge of econometrics and statistics, an awareness of measurement errors, testing for zero frequency, seasonal and periodic unit roots, analysing fractionally integrated and long memory processes, estimating VARFIMA models, using and interpreting cointegrating models carefully, choosing sensibly among univariate conditional, stochastic and realized volatility models, not confusing thresholds, asymmetry and leverage, not underestimating the complexity of multivariate volatility models, and thinking carefully about forecasting models and expertisecointegration;unit roots;fractional integration;volatility;leverage;VARFIMA;asymmetry;forecasting models and expertise;long memory;thresholds

McAleer, M.J.

Oxley, L.

English

Research Papers in Economics

  1
 
Ten Things We Should Know About Time Series* 
 
 
 
 
Michael McAleer 
 
Econometric Institute 
Erasmus School of Economics 
Erasmus University Rotterdam 
and 
Tinbergen Institute 
The Netherlands 
and 
Department of Economics and Finance 
University of Canterbury 
New Zealand 
 
 
Les Oxley 
 
Department of Economics and Finance 
University of Canterbury 
New Zealand 
 
EI 2010-49 
 
 
Updated: June 2010 
 
 
 
 
 
 
 
* The first author wishes to acknowledge the financial support of the Australian 
Research Council, National Science Council, Taiwan, and a Visiting Erskine 
Fellowship, College of Business and Economics, University of Canterbury, New 
Zealand, and the second author acknowledges the Royal Society of New Zealand, 
Marsden Fund.   2
 
 
Abstract 
 
Time series data affect many aspects of our lives. This paper highlights ten things we 
should all know about time series, namely: a good working knowledge of 
econometrics and statistics, an awareness of measurement errors, testing for zero 
frequency, seasonal and periodic unit roots, analysing fractionally integrated and long 
memory processes, estimating VARFIMA models, using and interpreting 
cointegrating models carefully, choosing sensibly among univariate conditional, 
stochastic and realized volatility models, not confusing thresholds, asymmetry and 
leverage, not underestimating the complexity of multivariate volatility models, and 
thinking carefully about forecasting models and expertise.  
 
 
Keywords: Unit roots, fractional integration, long memory, VARFIMA, 
cointegration, volatility, thresholds, asymmetry, leverage, forecasting models and 
expertise.  
 
JEL Classifications: C22, C32.   3
1. Introduction 
  
The broad area of spatial econometrics and statistics contains time series as a special 
case, wherein the space dimension is defined as time. 
  
Time series analysis is crucial to the understanding of movements of variables over 
time in the social, physical and medical sciences. 
  
When asked about the meaning of life, the Dalai Lama was reported to have said that 
it was to be happy. 
 
In “Of Human Bondage” (by Somerset Maugham), Peter Carey decided there was no 
meaning to life. 
 
Although there is no definition of the meaning of life that will satisfy everyone, many 
would agree that a functional specification would almost certainly involve a time 
series dimension, such as an AR(1) process. 
  
Truisms such as “The old wheel turns and the same spoke comes up”, “We live, we 
pay taxes, we die”, and “The only certainties in life are death and taxes”, almost 
certainly arose through observing historical patterns in time series data. 
  
The purpose of this paper is to highlight ten things we should all know about time 
series, which should assist in understanding time series data, and maybe even some 
key issues in life. 
  
 
2. Ten Things We Should Know 
  
(1) Knowledge of Econometrics and Statistics is Essential 
  
Time series analysis can be quite complicated, especially at the multivariate level, so 
one should come prepared with an appropriate technical background. The benefits of   4
having a good working knowledge of econometrics and statistics for analysing 
economic and financial time series data will become readily apparent. 
  
(2) Be Aware of Measurement Errors 
  
Measurement errors can be prevalent in measuring data in the social sciences. Few 
variables are measured correctly, whether at low, high or ultra high frequencies, so be 
aware of the likely presence of measurement errors which can affect estimation, 
testing, forecasting, and any subsequent analysis.  
  
(3) Test for Zero Frequency, Seasonal and Periodic Unit Roots 
  
Many time series at various frequencies, especially in economics, are non-stationary. 
It pays to be aware of the implications of the presence of zero frequency, seasonal and 
periodic unit roots, how to detect them, especially in the presence of structural 
change, and how to deal with them once they have been detected. 
 
(4) Analyse Fractionally Integrated and Long Memory Processes 
  
Time series data may have no memory (static models rather than dynamic), short 
memory (moving average processes), exponential decay (autoregressive processes), 
infinite memory (unit roots), or long memory (fractionally integrated processes). 
Many time series in economics and finance possess long memory, which can be 
modelled by fractionally integrated models. 
  
(5) Estimate VARFIMA Models  
  
Many multivariate time series can be explained using vector ARFIMA models or their 
seasonal variants. There are numerous variations of fractionally integrated ARMA 
models, and choosing among them is not always entirely straightforward. The 
application of various diagnostic checks can prove useful. 
  
(6) Use and Interpret Cointegrating Models Carefully 
    5
When time series processes are non-stationary, one or more cointegrating 
relationships may explain how the variables move together over time. It is easy to 
misunderstand the meaning and interpretation of cointegrating models, especially as 
alternative models are non-nested (such as either the levels or logarithms of a variable 
being tested under the null as I(1)), so cointegration tests should be used carefully. 
  
(7) Choose Sensibly Among Univariate Conditional, Stochastic and Realized 
Volatility Models 
  
Financial data have returns that may be unpredictable, but their volatility can be 
modelled as stationary processes and forecasted for purposes of risk management and 
forecasting Value-at-Risk. There are some similarities but many differences among 
alternative univariate and multivariate conditional, stochastic and realized volatility 
models, so care should be exercised in choosing from the portfolio of alternative 
volatility models. 
  
(8) Do Not Confuse Thresholds, Asymmetry and Leverage in Volatility 
  
Alternative models may have symmetric, asymmetric, leverage or threshold effects on 
volatility arising from positive and negative shocks of equal magnitude. It is easy to 
confuse asymmetry and leverage, in particular, even for univariate processes, but 
especially for their multivariate counterparts. This confusion is evident in textbooks, 
and sometimes in widely used econometric software package, which will lead to 
misinterpretation in empirical analysis. 
  
(9) Do Not Underestimate the Complexity of Multivariate Volatility Models 
  
Extensions of univariate volatility processes to their multivariate counterparts can be 
very complicated from the theoretical, statistical and computational perspectives. Not 
all models are created equal. Not all multivariate volatility models make sense, 
especially in terms of leverage, and time-varying covariances and correlations. 
  
(10) Think Carefully About Forecasting Models and Expertise 
    6
One of the primary purposes in modelling time series data, especially in economics 
and empirical finance, is to provide accurate forecasts. The models underlying 
forecasts should be investigated carefully, especially if they are given by experts, who 
frequently emphasize their own expert knowledge and intuition in obtaining 
necessarily biased non-replicable forecasts, over replicable forecasts, which would be 
based on an econometric model, which can lead to unbiased forecasts. Sometimes 
such reliance on expertise may be warranted, but at other times it is not. 
  
3. Conclusion 
  
There are many things in life that can be tiring and bothersome. Leamer (1988) lists 
ten such “bothers”. McAleer (1997, 2005) and McAleer and Oxley (2001, 2002, 
2005) suggest ten commandments that should be followed in organizing a conference, 
attending a conference, presenting a conference paper, for academics, and for ranking 
university quality. Most of these commandments are routinely ignored, in practice, 
but that does not make the need to emphasize them any less compelling. 
 
Nevertheless, we cannot ignore the fact that “We live, we die.” 
  
We should also not ignore the ten things we should know about time series. 
  
 
Acknowledgements 
 
The authors would like to thank many former (time t-1) instructors, and past (t-1) and 
present (t) students, for their patience and understanding, especially in all things 
related to time series.   7
 
References  
 
Leamer. E.E.  (1988), Things that bother me, Economic Record, 64, 331-335. 
 
McAleer, M. (1997), The Ten Commandments for organizing a conference, Journal 
of Economic Surveys, 11, 231-233. 
 
McAleer, M. (2005), The Ten Commandments for ranking university quality, Journal 
of Economic Surveys, 19, 649-653. 
 
McAleer, M. and L. Oxley (2001), The Ten Commandments for attending a 
conference, Journal of Economic Surveys, 15, 671-678.  
 
McAleer, M. and L. Oxley (2002), The Ten Commandments for presenting a 
conference paper, Journal of Economic Surveys, 16, 215-218.  
 
McAleer, M. and L. Oxley (2005), The Ten Commandments for academics, Journal 
of Economic Surveys, 19, 823-826.  
 

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