Suppose we have two independent variables, for that what should be the minimum no. of observations and is there any rule for this?
It depends on the modelling approach that you plan to use and the purpose of your analysis. For autoregressive integrated moving average (ARIMA) models, the rule of thumb is that you should have at least 50 but preferably more than 100 observations (Box and Tiao 1975). The primary driving force behind these numbers is that if there are seasonal components, you'll need several years worth of monthly observations to appropriately model that out.
On the other hand, if you are using a OLS regression-based approach, then arguably 4 observations may suffice (Simonton 1977).
References:
Box, G. E. P., and G. C. Tiao. 1975. Intervention analysis with applications to economic
and environmental problems. Journal of the American Statistical Association 70: 70{
79.
Simonton, D. K. 1977. Cross-sectional time-series experiments: Some suggested sta-
tistical analyses. Psychological Bulletin 84: 489{502.
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All Answers (18)
3rd Mar, 2015
Ariel Linden
Linden Consulting Group, LLC
It depends on the modelling approach that you plan to use and the purpose of your analysis. For autoregressive integrated moving average (ARIMA) models, the rule of thumb is that you should have at least 50 but preferably more than 100 observations (Box and Tiao 1975). The primary driving force behind these numbers is that if there are seasonal components, you'll need several years worth of monthly observations to appropriately model that out.
On the other hand, if you are using a OLS regression-based approach, then arguably 4 observations may suffice (Simonton 1977).
References:
Box, G. E. P., and G. C. Tiao. 1975. Intervention analysis with applications to economic
and environmental problems. Journal of the American Statistical Association 70: 70{
79.
Simonton, D. K. 1977. Cross-sectional time-series experiments: Some suggested sta-
tistical analyses. Psychological Bulletin 84: 489{502.
10 Recommendations
3rd Mar, 2015
William H. Fisher
University of Massachusetts Amherst
Ariel is correct. the problem with 50 is that, depending on what your time units are, you may not have enough data to capture and deal with periodic effects such as seasonality. Just one point -- ARIMA strikes me as fraught with all kinds of issues that can be hard to address. You might want to explore autoregressive Poisson models. Stata has a a program that will do that (arpois). The number of data points is still an issue for the practical reasons mentioned.
1 Recommendation
3rd Mar, 2015
Ariel Linden
Linden Consulting Group, LLC
I am not a fan of ARIMA because of its "clunkiness" and poor reliability between users in finding the correct model (even trained analysts got it right only about 25% of the time in one study). arpois is a good command for count data.
3rd Mar, 2015
Naveed Ahmad Lone
Islamic University of Science and Technology
Thanku sir,
sir actually i want to estimate the impact of domestic fuel prices over general prices level, within time period from 1991 to 2014 and the data is available both monthly as well as yearly, sir what would be the better option as per modelling is concerned
3rd Mar, 2015
Ariel Linden
Linden Consulting Group, LLC
Which technique for you to use is a matter of both taste as well as empirical reasoning. For example, you have sufficient monthly observations to perform ARIMA, but that doesn't mean that regression is out of the question. You need to do some basic data review to determine the amount of autocorrelation you have in your data, as well as the presence of seasonality.
I am attaching a link to a paper I wrote on time series analysis a long time ago. This may help you think about your approach.
I hope this helps
Ariel
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3rd Mar, 2015
Kurt Barbé
Vrije Universiteit Brussel
It depends on the frequency resolution you require. If you model your data with a specifiic model let us say for simplicity an ARMA model, then you have a numerator and denominator. The poles and zeros are the respective roots of the denominator and numerator. The frequency spacing of these poles and zeros (i.e. the phase of the poles and zeros) in the z-domain must be smaller than the frequency resolution of your data which is 2\pi/N. If you frequency resolution gets too large compared with the pole/zero spacing you get finite sample bias errors. For a thorough investigation, please consult: https://www.researchgate.net/publication/235417376_Fractional_models_for_modeling_complex_linear_systems_under_poor_frequency_resolution_measurements
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8th Aug, 2015
Asmaa Mansi Yaseen
University of Kansas
Dear I would like to ask a question within this regards
what if we want to use unrestricted VAR with annual data ?
1 Recommendation
11th Nov, 2017
Nibir Nath
Indian Institute of Technology Bombay
Hi Ariel,
You are saying that the thumb rule is to use at least 50 data points for ARIMA model, can you refer to some journals or articles for that? I will be highly obliged if you attach any reference for that.Thanks in advance.
1 Recommendation
12th Dec, 2017
Ben Osongo
University of South Florida
ARIMA models in the presented scenario has its pitfalls! I want to share a really defensible approach ( that premises on taste and empirical reasoning) in Stata
1 Recommendation
3rd Mar, 2019
Rajnikant L Mehta
University of Birmingham
Dear All,
Many thanks for all your suggetsions.
Regards,
Raj
4th Apr, 2019
Benny Van
Lincoln University New Zealand
I find the question is useful to my study. Thanks for all responses
4th Apr, 2019
Rajnikant L Mehta
University of Birmingham
Hi,
I'd also recommend that the time intervals are equal length and that you have 10 time point recordings before and 10 time points after a time point of interest.
Regards,
Raj
5th May, 2019
Khanh Hoang
Lincoln University New Zealand
According to the Central Limit Theorem, a conservative definition of a sufficiently large sample size is n greater or equal 30 (David F. Groebner, Patrick W. Shannon , Phillip, and C. Fry, Business Statistics - 9th edition, chapter 7).
However, depend on different approaches and research methodologies, the minimum sample size might be significantly differ. In general, the larger the better. You can transform your data from yearly to monthly data to have more data points.
5th May, 2019
Rajnikant L Mehta
University of Birmingham
Where one is specifically wanting to apply Time series models, then I'd suggest one to have observed at least 100 observations. Also the time intervals to be equally spaced.
Best wishes,
Raj
5th May, 2019
Miguel Ángel Ruiz Reina
University of Malaga
In my opinion depends of the problem to solve. But in Economy is recomendable more than 60 observations (Lehmann, E., & Casella, G. (1998). Theory of Point Estimation (Second edition ed.). New York Berlin Heidelberg: Springer. doi:ISBN 0-387-98502-6). For monthly data at least 5 years.
10th Oct, 2019
Vaibhav Agrawal
Sydney Airport
A Nice read:
https://robjhyndman.com/papers/shortseasonal.pdf
1 Recommendation
10th Oct, 2019
Miguel Ángel Ruiz Reina
University of Malaga
Thank you! Good contribution :)
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