Time Series Econometrics - Science topic

Yes it is

For selecting lag length: Use information criteria like AIC or BIC to determine the optimal lag length in your VAR/VECM model.

For testing co-integration: Employ tests such as the Johansen test or Engle-Granger test to assess co-integration between variables.

For VAR/VECM with non-stationary I(1) data: Implement the VAR or VECM model directly on the non-stationary data, as these models can handle I(1) variables without differencing.

To calculate the entropy measure of product/business diversification in STATA, you can use the trade entropy index. The trade entropy index is defined as the sum across destinations of the squared export shares for the region under study to all destinations. You can also calculate geographical sales dispersion by using entropy index of company sales per country.

In EViews, a static forecast is a one-step ahead forecast that uses the actual value for each subsequent forecast. A dynamic forecast is a multi-step ahead forecast that uses the previous forecasted value of the dependent variable to compute the next one.

As for which gives the most accurate forecasts, it depends on the data and the model used. In general, dynamic forecasts are more accurate than static forecasts. However, it is always important to evaluate the accuracy of both methods before making any conclusions.

The ARDL bounds test assumes at most one long run levels relationship. It does not test for multiple long run relations. The Johansen test can test for multiple cointegrating relationships. The difference is that the Johansen procedure assumes all levels variables are I(1) whereas the ARDL procedure assumes the dependent levels variable is I(1) and the independent variables can be I(1) or I(0). Using both tests may be useful if there is uncertainty over the orders of integration of the levels variables and the number of long run relations. If you are certain all levels variables are I(1) you only need to use Johansen. If you are certain there is one long run levels relationship and uncertain over the independent variables' orders of integration you only need to use the ARDL test.

Dear Professor, I know how to run the quantile regression. You can read the detail of my problem. I'm wondering if I can improve the performance of the model or alternatively change another model

The comparison between the two models may provide insights into how the variables respond to short-term shocks and how they adjust back to their long-run equilibrium relationships I think.

sir, i am doing research on labour market discrimination. help me to perform decomposition in unite level cross-section data.

Hello Dear Imran,

Were you able to find the code of steps for this methodology? Could you please share if you did?

Dear Stelios Xanthopoulos,

Interesting question.

The dummy variable reflects non-quantifiable effect that cannot be captured by the model. In your case policy changes can be addressed through dummy variable. Equating dummy variable with omitted variable may not be in order - the observation you got may not be generalizable.

A way to deal with this problem is finding the trends before and after by fitting to a linear, quadratic, ... curves as well. However it is enough to confirm existence of change point using a test like Mann-Kendall.

I will answer this question by suggesting that you consider your basic model.

1. You have a strange mixture of nominal, real variables and growth rates.

2. Interest rates are the equivalent of log differences

3 If the growth rate of M4 is non stationary this implies that the log of M 4 is I(3). I find this hard to believe.

4. Are there seasonal effects in your data?

5. I would be very doubtful if ARDL is valid in your case.

6. If I understand correctly you intend to identify your system by using a particular ordering of your variables. It will be difficult to justify any particular order

7.I would be concerned that you might have trouble accounting for bubbles in house prices and subsequent falls. The 20 years that you are using was a very difficult time for house prices and they were out of equilibrium for a lot of this period. Your project is very ambitious.

8. I would recommend that you talk to your supervisor and agree an analysis that might be more feasible..

Mr a. D.

The ECT(-1)os always the lagged value of your dependent variable.

Regards

The Students T-test (or t-test for short) is the most commonly used test to determine if two sets of data are significantly different from each other.

OlaOluwa Simon Yaya Olusanya E. Olubusoye Oluwaseun Aramide Otekunrin Adedayo Adepoju Hammed Abiola Olayinka Toheeb Aduramomi Jimoh

Dear Irfan sahib, the models under null and alternative should be nested to apply the Likelihood Ratio test and both should be based on same number of observations. In your case the number of observations are different so this issue cannot be solved by a hypothesis test. Rather you can use other ways to solve this. For example check if the value of parameters are drastically changed by including outliers or check if the the persistence (alpha +beta) of GARCH variance is changed significantly. If no drastic change occurs, outliers are not to be worried.

Sorry Valeriia, can you better explain the data and goal? Does the "train" contain a single time series (i.e. it is a vector) or many (i.e. it is a matrix)? For example, I see that you select 6 rows and all the columns (hence I think that train is a matrix with many time series) for fitting the GARCH model. First, I am worried that 6 rows are not enough to obtain an accurate estimation. Second, only one column (a single time series) should be selected if you fit a univariate GARCH model . Third (maybe it is my fault), I did not get what you mean by "I need to shift and change a number manually train[(9),train[(8),train[(20),...".

Unemployment is the dependent variable and ALMP's are the independent variables... Try to execute a simple regression model on R then Interprete how the independent variable affects the dependent variable.

Best!!

Check https://www.investopedia.com/articles/trading/07/stationary.asp

R-H bicorrelation test -https://faqs.tips/post/rolling-hinich-bicorrelation-test-can-anyone-help.html

@Fady M. A Hassouna and Kehinde Mary Bello, The augmented dickey fuller test is a conventional unit root test which does not account for structural breaks. Unlike, Lumsdane and pappel, Narayan and popp, Lee and stracizich and other unit root test that account for structural breaks.

Sigmasq is sigma square of the distribution of residuals which is considered as a proxy of the variance of the distribution of the dependent variable. Indeed this distribution is necessary to maximum liklihood method

Sigmasq is estimated in the second step after estimating the parameter related to estimators

Otherwise, SE is the standard error of regression which is the average of differencesome between actual values and fitted values of the dependent variable

Ibrahim Niftiyev , probably the reviewer wants to see not only whether a variable affects or not the other (i.e. the results of the Granger causality tests), but also to which extent (the magnitude and temporality of the dynamic relationship, something you can obtain from the IRFs of a VAR model). If you want to apply a VAR but you have a small sample size/data limitations, you want to consider a Bayesian VAR. Bayesian VARs are very popular and Bayesian methods are valid in small samples.

check Wilfredo Palma's book

dear Oyetoun Dunmola

As you can see from the screenshot, I have mixed results which is the exact reason that makes me confused. Which means that some of my independent variables have positive, some negative impact.

Best

Ibrahim

You might want to see the following:

Dear Mr. Niftiyev, your dependent variable varies betweem -2,5 and +2,5. Hence, it is better to employ a Tobit, Probit or Logit approaches if possible. The choice between these three approaches depends mostly on the distribution patterns of the variables.

ARDL/ NARDL QARDL and some other versions of ARDL usually have the preconditions of cointegarion which can be achieved when the dependent variable is I(1) and at least one of the independent variables too is I(1). You can read the original papers the established these techniques, you will observe the model used for testing the method is a contigerated one .

As a practitioner, I am sympathetic with the advice to "try all possible options to be on the safe side for unit root tests". However, if you obtain contradictory results, then you need to think theoretically about the time series being modelled. The ADF (etc.) with no constant (drift term) and no deterministic time trend is testing for a pure random walk (i.e. a model in which the variable is purely stochastic and can thus go anywhere, in which case the best predictor of the future value is the current value). Some variables, e.g. currency values, are like this. However, real economic variables are not purely stochastic but also respond to fundamentals. In this case, a random walk with drift is an appropriate univariate model: the drift term captures the deterministic impact of economic fundamentals (giving the variable a tendency to move up or down in every period); while the unit root captures the stochastic component (which may either reinforce or offset the deterministic drift term in any given period). Philosophically, this is appealing: we live in a universe that is neither completely deterministic nor completely random. Finally, it is possible that the stochastic component of the evolution of a variable may unfold around not only a drift term but also a deterministic time trend. So test for this as well. In conclusion, these possibilities should be considered in advance of running tests. And in all cases, look at the graph of the variable to be tested!

Zeynep Köylü Thank you!

Best

Ibrahim

I presume that your data is quarterly or monthly as otherwise, you have too few observations to make any reasonable inferences.

If you are trying to make causal inferences (e.g. you have an economic model that implies that x causes y and you wish to measure that effect). the CUMSUMSQ is one test that indicates that your model is not stable. Either the coefficients or the variance of the residuals is not stable. You have indicated that there is no heteroskedasticity so it is possible that the model coefficients are the problem. The test itself only indicates that there's instability and does not say what the instability is or what causes it. There are many possible causes of instability, (omitted variables, functional form, heteroskedasticity, autocorrelation, varying coefficients etc.) Your best procedure is to return to your economics and work out how your theory might lead to stability problems. Are there possible breaks in your data caused by policy changes, strikes, technological innovations, and similar. that might be covered with a dummy variable or a step dummy.

If you are doing forecasting (or projections) I would not be too concerned about specification tests. It is very unlikely that an unstable model will forecast well. You may achieve good forecasting results with a very simple model that need not be fully theory compliant.

Are you attempting prediction or are you trying to do some form of “causal” relationship. If you are estimating a ”causal“ model you conclusions are conditional on the model estimated. Strictly speaking, it would be better to use the adjusted degrees of freedom - particularly with your small sample. In this case, a non-significant coefficient does not necessarily imply that the coefficient is truly zero. It is more likely that your sample is too small t establish a significant result. Its p-value must not be very far from your significance level. If the estimate is of the sign and magnitude expected by theory I would accept the value and report the p-value. Esimating 5 coefficients is a big demand from a sample of 23 obs.

If you are simply doing prediction or forecasting and are not attributing explanatory power to your coefficients you might be better with a simpler model which might have better predictive ability.

Dear Ibrahim Niftiyev ,

Econometric models estimated with non-stationary data are profoundly invalid and misleading (Greene, 2002). An example of a simple scenario: - in a regression with one regressor, there are three variables that could be stationary or non-stationary; namely the dependent variable (Y), the regressor (X), and the disturbance term (u). A suitable econometric treatment of such a model depends critically on the pattern of stationarity and non-stationarity of these three variables (incl. the dependant variable). Since quite often variables can be non-stationary at I(0), it is important to understand the forces behind such non-stationarity, which largely include structural breaks, deterministic trends, and stochastic trends. Differencing (including the explained variable as in your case) is a common appropriate in nonstationary models, and this is often correct (Granger & Newbold, 1974; Green, 2002; and Stock, James & Watson, 2011).

Granger, C. W. J., and Paul Newbold. 1974. Spurious Regressions in Econometrics. Journal of Econometrics, 2(2):111-120.

Greene, W. 2002. Time series Models. (pp. 608-662) In Econometric Analysis, 5th edition. Prentice Hall, Upper Saddle Rive, NJ.

Stock, James H., and Mark Watson. 2011. Introduction to Econometrics. 3rd ed. Boston: Pearson Education/Addison Wesley.

The instruments used for the level equation are the lagged first-differences of the time-varying variables. These instruments are valid as long as

a) the idiosyncratic shocks are not serially correlated

b) the correlation between these variables and the individual effects is constant, i.e. a stationarity assumption is met

Dear all,

you can use as much as you whish but be carefull to the multicolinearity

best

If you provide a plot with the time series you have and illustrate how the break occurs, it will be easier to answer. The assumptions about et are not really plausible. I would apply log to both sales and price first.

But the major issue here is in how you understand the intercept break. So the first step is visual analysis.

Also, one approach to test your hypothesis is to conduct an MC experiment where you not the data generation process and then check if your estimates really correspond to the true parameters you used to generate data (this approach has been successful in crashing the belief in a number of well-known methods). You can google for it, but it is known that replacing missing data with dummies leads to biases, and it was demonstrated using an MC experiment.

First generation panel data analysis often assume cross sectional independence, i.e the shock to a variable in a country will not have any effect on the other countries variables. However, as a result of globalization and other related cross nation interlinks, it is apparent that a problem in country A can affect country B. Most of the conventional panel analysis like fixed effect, Random effect, Panel ols, among others fall into this category. In order to correct the bias in the estimate of 1st generational panel analysis, the 2nd generational panel analysis was invented. This methods appropriately incorporate the cross sectional dependence in the modeling. This includes methods like ccemg, cs-ardl, cup-FM and so on..

To justify the employabilty of ARDL-Bounds tests approach,the results from ADF and PP stationarity tests should indicate the variables were not integrated of the same order.

To answer to criticism of spurious regression, if it is time trended. Causality is still a bigger issue than just uncovering stationarity of time dated series. We need the theory to guide us and the use of statistics in experimental research design to handle causality is still not resolve.

In standard applied econometric modelling practice, it is advisable to run as much diagnostic tests as possible to optimise model performance/estimates, but being cautious about running tests that are applicable/relevant.

Dear Ibrahim,

I also recommend Greg. N Gregorios and Raven Pascalau @Hamid Muili and google for more materials on non-linear relationship.

Regards

logging variables does not remove unit root from a series, it only smoothens the line a bit and make interpretation easier as it will be interpreted in percentages.

Reporting either ADF or PP is at your own discretion. But for confirmatory purpose you can report both ADF and PP unit root test as well as KPSS stationarity test provided your variable does not have a structural breaks.

Furthermore, Using 11 variables might be too much except you have a very large dataset say 100 or more. Because using a large variables on s sample size shrinkens the degree of freedom which might affect the true inference made from the estimation

Best Regards

Hi Sarah,

Estimates from the VEC model are presented in two components. The first component of the model contains results of the long-run epoch, while second segment of the model contains results computed based on the second step of VAR in first/and or also second differences, including the error correction term (ECT) estimated from the first-step Johansen procedure. The error correction or cointegration term measures/shows the speed of adjustment at which a deviation by the specified endogenous variables from the long-run equilibrium path gradually corrects through a sequence of partial short-run adjustments. In other words, the error correction term shows the long-run behaviour of specified endogenous variables towards convergence to their long-run cointegrating relationship. The occurrence of steady adjustment to the long-run equilibrium through the short-run partial adjustment mechanism by examining the statistical significance of the respective variables to deviations from the long-run equilibrium path.

In my view, if you conducted all essential residual and stability diagnostic tests (including the roots characteristic polynomial VEC model stability test) and they seem fine, then I don't think your results are over-estimated, as long as your results are also consistent with the relevant economic theory/theories underpinning your empirical research study.

All the best!

Schwarz-Bayesian, (SBC), vector Hannan-Quinn, (HQC) and the likelihood ratio (LR) can also be used.

Hello,

you can try

Well, Your CUSUM results indicate that the linear model is inappropriate to be estimated as this indicates some nonlinear behaviour. I would suggest the the use of nonliner model. I f you want to test for cointegration, use nonlinear cointegration analysis of Seo 2006 or even some new developed nonlinear cointegration analysis.

Regards,

Dr Katleho Makatjane

Business and Risk Analyst

Basetsana Consultants

You haven't mentioned glmmTMB in your pro/con description, though you mention it in the title, so I'll add some pros for this package. The advantage of glmmTMB is that you can easily model complex / nested / cross classified random effects structures and you have different correlation options (like AR1 etc.).

Furthermore, you have various diagnostic options for glmmTMB as well, to quote from another thread:

You could use the "performance" package to calculate indices like r2() or icc() [1]. You can also check your model for overdispersion or zero-inflation with the "performance" package (check_overdispersion() or check_zeroinflation()). Furthermore, it can create diagnostic plots (which requires the "see" package for plotting capabilities [2]). Another, imho important, package in this context is "DHARMa" for residual diagnostic plots [3].

Finally, a comment on your model design: when analysing longitudinal data / repeated measurements, I'd suggest adding the time variable both as fixed effect and random slope. And I would treat "year" as continuous, maybe using a quadratic / cubic or spline to model time variation, so you would have something like:

model <- glmmTMB(y ~ x1 + year + (1 + year | site))

or

library(splines)

model <- glmmTMB(y ~ x1 + bs(year) + (1 + year | site))

As estimates for splines / cubic / quadratic trends are somewhat difficult to interpret, I suggest effects plots ("estimated marginal means"), which you can easily produce with the "ggeffects" package [4].

[1] https://easystats.github.io/performance/

[2] https://easystats.github.io/see/articles/performance.html

[3] http://florianhartig.github.io/DHARMa/

[4] https://strengejacke.github.io/ggeffects/

Farooq Shah I do not think you are able to use GARCH if there is no ARCH effects on your data. However, first try to estimate an OLS and check for the ARCH effects even though is statistically wrong, because you use OLS which assumes constant variance and test for ARCH effects.

Try the Box Test too to check whether you have autocorrelation in the residuals.

Begin with a simple model AR(1)-ARCH(X) and than see if you can estimate a GARCH.

These are the estimates of parameter for the independent variable. So it is mean effect for each variable. Not County specific. You can use this for all country. For country specific intercepts for example in a fixed effect model, you can search using fixef command. fixef(your model name)

There exists very many unit root tests, and sometimes these tests can give conflicting results, for instance, of whether a particular time series is a I(0) or I(1) process [or I(1) / I(2) process]. In this case a researcher should either have an a-priory preference for a particular unit root test (say, DF with a trend or without a trend) or use an expert judgement on whether a particular time series is or not stationary.

But, of course, a conclusion of whether there is a bubble in a particular financial market is also subjective on its own, and cannot be strictly based on a result of one particular unit root test or even combination of these tests.

You have to perform bound test which indicates if you have a long-run or a short-run of the variables, if there is only short-run you perform the ARDL for the short run , if there is co integration you should proceed with VECM or ECM depends on the results that bound test shows Srikanth Potharla

I can recommend "Elements of Nonlinear Time Series Analysis and Forecasting" by Jan De Gooijer. It was published by Springer in 2017. It provides a description of the different nonlinear time series models with many references, examples and also pieces of code. It covers parametric and non parametric approaches for univariate models and even a few multivariate models.

Hi, my answers to your questions:

1. No, it is not compulsory but...if you do not do something to deal with the seasonal behavior of your data, your estimates will be reflecting two effects: those coming from common seasonality and any other effect that is not seasonal and that could be linked to your tourists arrivals. So, if you want to get a deeper understanding of the spillovers in tourist arrivals, beyond those contained in seasonal effects, you will have to deal with this seasonality in some way: one way is to estimate your VAR with and without seasonal adjustment in your data. That will help to see how the seasonal patterns affect your results. Another avenue would be to include seasonal dummies as exogenous variables in your VAR. I would suggest to follow all these three approaches to have a more comprehensive view of what is going on.

2. Taking 12-month seasonal differences is one of the simplest and most intuitive ways to try remove the seasonal pattern in your data. Sometimes it helps a lot, some other times it does not help. Let me explain one of the problems with this approach. Most of our times series can be thought of the sum of at least two components: a seasonal componen s(t) and a non seasonal component x(t). So lets say that your series looks like this: y(t)=x(t)+s(t). Once you take the 12 month difference you have y(t)-y(t-12)=x(t)-x(t-12)+s(t)-s(t-12). The good thing is that now you have removed the seasonal component from s(t)-s(t-12), nevertheless, the cost you pay is to GENERATE a previously nonexistent seasonal component in the term x(t)-x(t-12). So, you try to solve a problem just to generate another one.

I agree with the previous response, this is probably one of the reasons why the airline model does a good job when forecasting series in 12 month differences.

Hope it helps!

Analysis of mixed variance and variance using SPSS by Dr. Samir Khaled Safi on 7/7/2019

Hi,

Please see these attached links:

Best

Dear Richard Collins,

Indeed, my discussion note is rather general. I am using a new term, 3D Vector Plurigrafity, in order to promote a new quality of graphic modeling based on statistical analysis. I am referring in my discussion note to the challenge of using form, color, and changes (or shifts) in vector graphics to portray complex phenomena as they evolve or, more specifically, as their analyses evolve. 3D is not a term I endorse for most anything plastic, since a 3D grid without the time factor, not to mention color, is already 3D, however static. 3D Vector Plurigrafity is a process, not an object.

If you conduct a search for my name, you will find a comment to one of my articles, on Brexit, saying that it is dated. In fact, the paper was a short synthesis paper, graded summa cum laude by University of Mainz, uniting much of the available research on the linkage between Brexit and migration before the popular EU referendum. And I changed my mind about the UK leaving the EU.

The Internet, contrary to your allusion, is not an absolute reflection of the world as a whole, and when it comes to the Brexit discussion, which has nothing much to do with my discussion note, it is more question of the National Health System (NHS) and other sectors than the online world.

I disgree with your judgement that ResearchGate is disorganized. Since you provided a factual comment, I am quite sure you are an academic capable of drawing conclusions as to my discussion note, which you did. I grant you that. And I grant the ResearchGate algorithm that you were selected.

Composite words as in German are rare in English, and are often reduced to parts of their original elements, take 'Edutainment,' for instance. As long as a new term is defined, which I think is sufficiently the case with 'Plurigrafity,' or more fully 3D Vector Plurigrafity, given my note along with my comment, I do not see why, per se, it should not be a lasting word. Of course, you have the right, as everyone, to forget, Richard Collins. I thank you for your reply.

Sincerely

Thorsten Koch, MA, PgDip

You need the correlation matrix to check the relation between the response variable and explanatory variables and investigate the multicollinearity among explanatory variables. If your data is time series I think you need to check ARIMA with exogenous variables.

Dear Murat Tuna

If Arch-Garch test appear significance where p-value =. 000 that is mean presence of heteroskedasticity problem you should examine residuals series if there is a period of high volatality followed by period of low volatality and so on. In this case you should estimate GARCH famlily model.

When N > T then cross sectional issues such as fixed effects and random effects become more important because cross-sectional variation in the data dominates than within variation (time series). Moreover, usually study average the data over 5 year and time dimension becomes less important.

Yes it is appropriate to ignore the time dimension in unbalanced panel with cross-sectional units greater than time period.

Hi, I have a related question to this topic. Currently I'm working in a time series anylsis, the first ADF test with raw data I didn't consider any lag and all the results where nonstationarity. After this I runt eADF test for the first difference and the are stationarity, but I also run the test with lags according to the varsoc test and the first difference and they also non stationarity. Wich should be the right process. Thanks

Please from your data collected, it is a time series data. Instead of performing statistical test using Stata, SPSS, SAS, R, etc, i will strongly recommend that you perform econometric test such as Unit root test, Johansen Cointegration test, Granger tests, and Ordinary Least Square regression. The most suitable software that i will recommend is the Eviews software.

Time series data are often known to be non-stationary, thus a unit root test should be performed to turn such non-stationary data into stationary at first difference or in rare cases, second difference. The reason is that data for oil price, inflation, industrial production, FX, stock index and so on, were collected from secondary sources and must have been measured in different unit.

Use Eviews (Econometric views) software for your analysis.

Best regards

Owan

Normality is assumed for convenience in linear regression models, but it is not necessary.

The Gauss-Markov Theorem, which is a sufficient condition for OLS to be BLUE, does not assume normality.

Kruskal's Theorem, which is a necessary and sufficient condition for OLS to be BLUE, does not rely on normality.

If one is concerned about non-normality, the Box-Cox transformation can be used as a filter to transform both non-normal and heteroskedastic errors.

I don't think your model makes sense. Why is z/gdp in the model instead of just z? If you do a little algebra on your model the actual model has a function of gdp on the lhs. I don't know what function because you give no information on your variables, If say your eqn is z=ax +by nobody can really help because there is no real information. David Booth.

Thank you for the references Mariel Gullian Klanian , finally I've finished my research project for undergraduate thesis

You might try R. Tutorial here: https://www.youtube.com/watch?v=dc1L3zjsgiY

R, of course, is free.

Guechari Yasmina , Anton Rainer and Salman Haider thank you all, for your valuable feedback. I will try and apply each recommendation.

Dear SC Thushara,

I'm not sure about your question, but I think I've read about it in:

https://pdfs.semanticscholar.org/b1cd/c8da3b994606ba4f96b8e0577e26f8dccd29.pdf?_ga=2.30146879.1241071524.1551216901-578234132.1551216901

Dear Ahmed, for your optimal lag length, you should first run a PVAR and from there you go to lag structure to see the optimal lag length chosen by the following information criteria: AIC, SIC, HIC, BIC. But I would suggest that you set a maximum lag length within which any of the aforementioned information criteria can choose the optimal lag automatically.

For your panel unit root test, there are various procedures that come together when you run the test. The LLC, IPS, Fisher-ADF, PP tests. If there is a mixed result of unit root test among those procedures, you can go with the outcome of the majority.

If your variables have unit root or they are non-stationary and require differencing, then you need to run a panel cointegration test to find out if long-run relations exist. The procedure for cointegration test is the Johansen-Fisher combined test and the Kao residual-based test.

For model comparison between fixed and random effects, you may have to run the Hausman model selection test.

I hope this helps...

in the case of GPH test, H0: d=0 short memory

if0<d<0.5 it indicates long memory, stationary .

so d=0,2 mplies long memory and stationary