Questions tagged [time-series]

statistical techniques for application to data whose observations concern an entity or phenomenon at different points in time.

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25 views

Cholesky Identification in Structural VAR

Can you suggest me a framework in macroeconomics or finance where identification of a Structural VAR model through Cholesky ordering is still considered credible (in your opinion)? I'm looking for a ...
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5 views

Converting from Quarterly to Monthly Data for Output Gap

I am currently working on the quarterly output gap data on FRED. However, I would like to convert the data series into a monthly one. Would an appropriate methodology be to divide the dataset by 3 ...
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1answer
23 views

Filling gap in data with correlated series

I have two time series, of different length. A time series is GDP growth. The gdp growth is the series I need, and it is also the longer series, but it has two gaps in two periods one after the other. ...
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32 views

Deflating value series in currency A with CPI based on prices in currency B?

Say we have time series data on the annual value of imports in the UK from the US (in US dollars). Would it be appropriate to deflate the latter using the UK Consumer Price Index (which is based on ...
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273 views

Does I(1) imply a process is cointegrated with its lag?

My question is about the definition of cointegrated. $y_t =y_{t-1}+u_t$ $u_t =\eta_t +0.5\eta_{t-1}$ where $\eta_t\sim N(0,1)$ is i.i.d. white noise. I claim that $y_t$ and $y_{t-1}$ are cointegrated ...
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1answer
41 views

Algebra for two period forecasting in AR (3) Model

I wondered if some folks could help fill in a knowledge gap for me with some time-series algebra please regarding the following AR (3): $$x_t = \phi x_{t-1} + \phi_2 x_{t-2} + \phi x_{t-3} + \...
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1answer
30 views

$I(g)$-terminology

During my studies I came across the $I(g)$-symbol, in the sense that $Z_t \sim I(g)$ for an integer $g$ and $Z_t$ is a times series. What exactly does this mean, and does it have to do with ...
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1answer
34 views

How to recognize correlation in spurious regression case

Assume we are given two independent random walks $$ Y_t = Y_{t-1} + \varepsilon_{1, t}, \quad \varepsilon_{1, t} \sim \mathcal{N}(0, 1) \\ X_t = X_{t-1} + \varepsilon_{2, t}, \quad \varepsilon_{2, t} \...
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1answer
29 views

Interpreting an ADF test in R

Although being a mathematician, I am fairly new to time series and R. On an assignment I was being asked to check a time series for stationarity in R, only using the $\texttt{adf.test}$ function that ...
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11 views

Quantifying treatment effect in multivariate interrupted time series

I have a multivariate time series dataset, from which I am building an ITS (Interrupted Time Series) model by using facebook's Prophet to construct the counterfactual. Let's say I have a y variable ...
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1answer
50 views

Stationary vs. Non-stationary data in a BVAR model

I am replicating a paper using BVAR model and I first I have run the model with non-stationary data. Then I just wanted to compare the results with stationary data and I launched the model but I get ...
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35 views

Frequency and time of a time series suddenly changed, are usual methods valid

I have a time series data that used quarterly information on a variable, but has now shifted to bi-monthly releases, from September 2008 to July 2021. This is a survey based measure, released at the ...
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1answer
60 views

Durbin Watson Test for an AR(1) process

$(1) y_t =\beta y_{t-1} +\epsilon_t$ $(2) \epsilon_t =\rho \epsilon_{t-1} +v_t$ Where $v_t$ is i.i.d white noise. I know that OLS estimates of (1) are biased. It would then follow that estimates of $...
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0answers
45 views

AR(q) Strongly Stationary

Consider an AR(q) process, $u_t$. If the roots of a characteristic polynomial are outside of the unit circle, the AR(q) process is weakly stationary. I've seen this proof that proceeds by showing the ...
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1answer
70 views

Estimation of variables

I am trying to estimate some variables, but I would like to know if what I am doing is right. I am using some data about labour productivity (in log) and, by using Stata, I filtered (Hodrick-Prescott) ...
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1answer
92 views

Finding consistent but inefficient GMM estimate

Consider the following linear model $$y_t = x_t' \beta +u_t$$ where $t =1,...,T$ and $x_t = (x_{1t} x_{2t} ... x_{kt})'$ , $ \beta$ is $k \times 1$ vector of unknown coefficients, $u_t$ is an iid ...
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2answers
32 views

Intercept in 2nd-stage Error Correction Model (ECM) regression — yes or no?

When doing a two-step ECM regression, do we add an intercept in the 2nd stage regression? I've seen course notes that add an intercept in the ECM, but some do not, so I'm confused if I should include ...
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1answer
33 views

K-step ahead forecast of VAR(2)

I am trying to determine how to write the K-step ahead forecast of a VAR(2), with two variables, as a weighted average of its mean and last observations. I understand that one must use companion form, ...
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35 views

IRF vs Autocorrelation function of AR(2)

Will the impulse response function and autocorrelation function of an AR(2) coincide? I say that they will not, because $IRF_{t}(t+k)$ (that is, the effect of a unit shock at time $t$, on the process ...
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15 views

Best method for extracting cycle component of time series

I have macroeconomic time series data, including both quantity and proportion variables (i.e. aggregate consumption, unemployment rate, etc.). I want to work with the rawest version of the data, ...
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1answer
22 views

How to obtain real money balances data

Theoretically real money balances ($m_t$) are defined as: $m_t=\frac{M_t}{P_t}$ Where $M_t$ are nominal money balances, and $P_t$ is the price index of the economy. If I were to make an empirical ...
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43 views

Detrending multiplicative model

I have a GDP quarterly series and IND.P monthly series, which I need to detrend. I am following Bernanke et al. paper from 1995 and the way they do it is: ...
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1answer
27 views

What does "sample period" in this case mean?

Dasgupta,2019 documented that the treated group comprises all firms that are headquartered in countries that have passed a leniency law by year t. The control group comprises firms in countries that ...
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72 views

How to handle the missing values' issue of newly listed stocks?

I am trying to test some asset pricing models on 10 portfolios for the period of 2010-2020. The problem is that three of these portfolios included stocks that are newly listed in 2017 and 2018, so I ...
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2answers
52 views

Examples of the use of Vector Autoregressive Models

I am self-learning Vector Autoregressive Models currently, and have practiced on a few datasets. But I wanted to read some actual research papers that use VAR, so that I get an idea of the level of ...
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26 views

What is the importance of moving seasonality in seasonal adjustment?

Both Stable and Moving Seasonality are computed in Sliding span test (or D8 F-Stat test) and M7 statistics. But what is the purpose of finding out the presence of moving seasonality in seasonal ...
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27 views

Modelling GDP growth rates with an AR(1) process

I am trying to model the growth rates of real output per worker. I read that GDP growth rates are often assumed to be stationary and are modelled using an AR(1) process, so I took logs and then took ...
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1answer
20 views

Nominal Values or Real Value & stationary

I'm going to estimate a time series regression which has consumption as a dependent variable. My data source give it in nominal form and unfortunately there are no other sources. It is Question : Can ...
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1answer
117 views

Converting monthly data to quarterly

I have monthly shock series, which I want to convert to quarterly form. I have seen several methods like taking average of 3 months or summing 3 months for making a quarter. I would like to know how I ...
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21 views

rebasing an index with inconsistent ratios between old and new data points?

I have a question about rebasing indices, hoping someone might be able to help. I'm working with two sets of index data for residential property prices from the Australian Bureau of Statistics. the ...
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0answers
21 views

Extract residuals from Uhlig's rejection method - Lag selection

I wanna determine the number of lags for a Baysian VAR/FAVAR model, which I implement based on R's VARsignR package. To compute the AIC/BIC I'd need the residuals of the model estimation. How can I ...
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1answer
35 views

Regressing (Very) Smooth Time Series

What are the possible problems/issues of regressing smooth time series with almost no fluctuation? Here is a specific example. Is there anything I have to pay attention to when interpreting ...
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30 views

Do you know how to compute the IRF of a GARCH (1,1)

We have the following model (GARCH (1,1) ) $y_t=\sigma_t\epsilon_t$ $\sigma_t^2 = \omega + \beta*\sigma_{t-1}^2 + \gamma*y_{t-1}^2$ Note that we can rewrite the latter as: $\sigma_t^2=\frac{\omega}{1-\...
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1answer
91 views

Should Prices (or Price Indices) be modelled with deterministic trend?

I always face a dilemma on whether to assume prices to have a time trend or not while modelling. It is also partly a statistics problem. Let me explain. Assume I have time series, $y_t$ of price of a ...
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1answer
450 views

Stationarity vs weak dependence

I am doing an undergraduate course in econometrics where we are using the text Introduction to Econometrics by Dougherty. While going through time series, it was mentioned that one of the necessary ...
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29 views

Could a time series be a pooled OLS?

Hello to everyone on the forum, I am currently working with intraday electricity price data. In the electricity market each hour is considered as a different product, because the demand and production ...
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25 views

Comparison of coefficients in log(y_t) and log(y_t/y_0) LHS specifications in LP-IV

I would have a question related to econometrics. Likely not all the details are needed, but please bear with me. My goal is to use local projection with an instrument to find out the response of an ...
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1answer
30 views

Stationarity, ADF/KPSS, Autocorrelation and Heteroscedastiy

i have a time series which is not stationary due to ADF/KPSS test, but is is in its first difference. So ADF and KPSS tell me it is starionary so it has a constant mean/variance/autocorrelation. But i ...
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23 views

Does GMM have any assumptions that you can't test empirically (and must instead argue qualitatively for)?

My understanding is that you can empirically test some of the main assumptions required for using a GMM estimator. Namely, I understand that you can test over-identifying restrictions with Hansen's J ...
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1answer
38 views

Variance in the Context of a AR (1) Model

I wondered if someone could help me in terms of the required algebraic steps from expressions (3) - (4), for the the moving average representation of the AR (1) below? Would be appreciated. $$y_t=a +\...
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1answer
144 views

Recursive Substitution in Time Series

Would appreciate some guidance on a matter of recursive substitution, where we have the AR model: $$y_t = \alpha +\theta_1y_{t-1}+ u_t$$ And $$E(y_t)= \mu_t$$ Where: $$\mu_t = (1+\theta_1 + \theta_1^2+...
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45 views

What type of econometrics is practised most?

This might sound like a weird question, but what type of econometrics is most common in academia and / or the private sector? Here I am thinking about time series econometrics (Bayesian and ...
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1answer
20 views

How does using HP filter allows us to estimate long-run values for variables such as output and unemployement?

I'm reading the paper "Okun's Law: Fit at 50?" written by Laurence Ball, Daniel Leigh and Prakash Loungani. In it, in order to estimate Okun's Law in its level form, they use the HP filter ...
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1answer
47 views

Should one remove trend from time series before testing for cointegration?

Should one remove trend from time-series before testing for cointegration? I guess no, but I couldn't find any answers yet. Also is it necessary to remove trend before estimating a VAR model if the ...
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48 views

Deconvolution in economics

Here it says In mathematics, deconvolution is an algorithm-based process used to enhance signals from recorded data. Where the recorded data can be modeled as a pure signal that is distorted by a ...
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25 views

Is it okay to difference data with different time intervals?

I have a question that is from an old project and that I want to clarify purely for future research. The question is, if you have a time-series that occurs at intermittent intervals, say once ever 4, ...
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1answer
184 views

ARIMA - reason for + MA term

I have 2 questions regarding ARIMA. 1st: How do we get the MA component - the et's (as we want to regress yt on lagged yt and also et and lagged et's)? If I want to regress yt on lagged yt's, I have ...
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4answers
352 views

Could you recommend a book or lecture notes about time series that is easy to understand?

What are some time series texts that you would recommend to start studying? Some easy textbooks/lecture notes or step by step for undergraduate level. I'm not so good at math/statistics.
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54 views

GDP per Capita in Panel Data: Must the base year be the same for all cross-sections?

I'm trying to run a small project using time series in panel data. One of the variables used is the GDP per capita for a few countries (the countries are the cross-sections). Is there a problem if the ...
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34 views

graph of dependent variable after years of restructuring in panel data

i'm not very able to use stata. For my thesis, I have a panel data(1970-2017) for different countries and a lot of variables. In this dataset, there is a dummy (dhairendH) that is equal to one in the ...