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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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Understanding the construction of stochastic processes

I've seen stochastic processes modeled/constructed in the following way. Consider the probability space $(\Omega, \mathcal F, Pr)$ and let $\mathbb S$ be the (measurable) transformation $\...
jmbejara's user avatar
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10 votes
0 answers
141 views

Replicating a state-space model

I am trying to replicate the results of Cochrane, 1998. Most of the paper is just describing the theory behind The Fiscal Theory of the Price Level. But from p. 42 he begins the econometrics aspect. ...
WoodfordJr's user avatar
8 votes
1 answer
5k views

How should one determine the proper number of lags in a time series regression?

I am using time series data in economic model estimation. I want determine proper lag for Error Correcting Model (ECM) model for example. I can check AIC, SC and HQ criterion for determine proper lag. ...
Huseyin's user avatar
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8 votes
2 answers
11k views

Why does slowly decaying ACF indicate that a time series is non-stationary?

I am a student studying time series econometric online and looking for help talking around some of the principles. There is one point I am trying to understand better. I've come across some ...
Adrian_P's user avatar
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7 votes
2 answers
269 views

Testing for serial correlation with General Regressors

This is from Introductory Econometrics (Wooldridge) 5th Edition page 420. Consider: $$y_t =\beta_0 +\beta_1 x_{1t}+\beta_2 x_{2t}+...+\beta_k x_{kt}+u_t$$ where $Cov(u_t, x_{jt})=0$ for all $j$ but ...
Michael Gmeiner's user avatar
7 votes
1 answer
4k views

White versus Newey-West standard errors

could you please help me to understand when I should use either white or newey-west standard erros? I do work with time-series data. I look at both contemporaneous and intertemporal realtionships. ...
frame's user avatar
  • 91
6 votes
3 answers
375 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 ...
Michael Gmeiner's user avatar
6 votes
1 answer
1k views

Why is VAR analysis all linear? Why not nonlinear?

When doing VAR analysis, it is almost always a linear form that gets used. Is there any justifying reason (most DSGE models are non-linear unless linearized) to use a linear form?
GADAN's user avatar
  • 61
6 votes
1 answer
115 views

Showing that a transformation is measure preserving

Note: This question is related to this question about the construction of stochastic processes. Specifically, it relates to the transformation $\mathbb S: \Omega \rightarrow \Omega$ that is mentioned. ...
jmbejara's user avatar
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6 votes
1 answer
179 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 ...
Dayne's user avatar
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5 votes
3 answers
107 views

Two variables: Which moves first?

Say I have a time series of two variables, $X$ and $Y$, and want to find out which one of these two moves first. One example is the one of GDP growth and investment growth, where we usually tell the ...
FooBar's user avatar
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5 votes
3 answers
298 views

Misspecified autoregressive models

I want to know the impact of misspecifying lag levels in AR models. Say the true model is AR(P), while in estimation AR(P-1) is estimated and used for forecast. What will be the impact of estimating ...
Daniel's user avatar
  • 71
5 votes
2 answers
579 views

Data mining in econometric modelling

Would I be "mining the data" in a time series analysis if I add more lags than theory suggests? For instance, for annual data analysis, it is recommended that two lags would be sufficient to capture ...
london's user avatar
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5 votes
1 answer
122 views

How do I construct the score process of a Markov model and verify that it is a Martingale?

The following is a specific question that is useful for demonstrating a general idea. Consider the following autoregressive model: $$ X_{t+1} = \alpha_0 + \beta_0 (X_t - \alpha_0) + W_{t+1}, $$ where ...
jmbejara's user avatar
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5 votes
1 answer
522 views

Missing values in economic time series

I am trying to run a time series analysis on some variables - GDP being my dependent variable, and my independent variables are oil revenues, government expenditure, exports and FDI inflows. My data ...
Bimz's user avatar
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5 votes
1 answer
144 views

Skepticism about the claims of instrument variable validity/exclusion through a statistical test—the Arellano-Bond Test

I am an applied researcher and occasionally come across papers that have panel data and that use dynamic models with both a fixed-effects term and lagged DV (or multiple autoregressive terms): $y_{it} ...
Student's user avatar
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4 votes
1 answer
2k 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 ...
CWK's user avatar
  • 43
4 votes
1 answer
310 views

What does one-sided polynomial on lag operator $L$ mean?

In some time series texts, there are some talks about one-sided polynomial on lag operator $L$. I tried looking up what this means, but I cannot find one. So what does one-sided polynomial on lag ...
Miam's user avatar
  • 59
4 votes
2 answers
251 views

Can PPP adjusted values be compared over time?

I'm a little baffled about this: Let's say I want to compare the average income of 2 countries, A and B. Of course I'm interested in the real income so I adjust to PPP using the big mac index of that ...
RiskyMaor's user avatar
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4 votes
2 answers
2k views

Why Is Cointegration Important In Practice?

In one of my econometrics classes. I'm nearly finished a problem set and assigned readings on an introduction to cointegration. I've essentially finished the assignment, run dickey fuller tests on ...
Adrian_P's user avatar
  • 157
4 votes
1 answer
125 views

VAR inversion - looking for a good resource

I am having trouble with something that should be pretty basic. I need to invert a VAR (vector autoregression). Everything I have read just brushes past the actual inversion process, taking for ...
aburn's user avatar
  • 43
4 votes
1 answer
69 views

Proof that a Unit Root process is Difference Stationary

Consider $$y_t =a_1 y_{t-1}+a_2 y_{t-2} +...+a_p y_{t-p} +\varepsilon_t $$ The characteristic polynomial would be: $$(1-a_1L -a_2L^2 -...-a_pL^p) $$ Suppose that there is a unit root, say that $L=1$ ...
Michael Gmeiner's user avatar
4 votes
2 answers
174 views

Year Fixed Effects in a Dynamic OLS Regression with Cointegrated Variables

I am estimating a dynamic OLS model since I have variables that are non-stationary, but cointegrated. In addition, the data is a standard time-series (i.e. one observation per one time period) so ...
guest123's user avatar
4 votes
1 answer
1k views

Demand estimation with a lagged dependent variable

Suppose I have the following structural equation for demand estimation in time-series: $$q_t=\beta_0+\beta_1\hat{p_t}+\beta_2incom_t+\beta_3q_{t-1}+\epsilon_t$$ Where $q_t$ stands for the quantity ...
John Doe's user avatar
  • 423
4 votes
1 answer
6k views

Conditional variance vs. unconditional variance in ARCH model

I am in the process of working through some problem sets. I have studied some time series, but my knowledge of ARCH models is pretty basic. I am given the following information: $Y_t = a_0 + a_1 Y_{t-...
jbrau's user avatar
  • 101
4 votes
1 answer
535 views

How to linearize the following difference equation?

I'm doing economic modelling where $x_t$ is the intertemporal cash-flow variable. I need to solve the following recurrence relation $$x_{t+1}=\frac{x_{t+8}}{x_{t+1}}$$ My problem is that I don't ...
Übel Yildmar's user avatar
4 votes
1 answer
315 views

How to approximate stochastic volatility model with finite-state Markov chain?

A common practice when computing solutions to stochastic dynamic optimization problems is to approximate an exogenous forcing process $z_{t+1} = \rho z_t + \sigma \epsilon_{t+1}$ with a finite-state ...
ivansml's user avatar
  • 1,096
4 votes
0 answers
37 views

Max Likelihood Estimators of a stable Gaussian VAR$(p)$ process. Are the Lutkepohl formulas correct?

In «New Introduction to Multiple Time Series», page 90, we have the following formulas for the ML estimators of a stable Gaussian VAR$(p)$ process: where $\tilde \alpha = vec(\tilde A_1,...,\tilde ...
An old man in the sea.'s user avatar
4 votes
0 answers
80 views

R reproducible example, restrictions on cointegrating equations

The code given below estimates a VEC model with 4 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor). ...
london's user avatar
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4 votes
0 answers
60 views

Non parametric and parametric tests of martingale?

A martingale is a model in which the expectation for the next value is equal to the presently observed value, even given knowledge of prior values, ie $E(X_{n+1} |X_1, X_2, ..,X_n)=X_n$ What tests ...
user157623's user avatar
  • 1,453
3 votes
1 answer
334 views

Stationarity in Time Series

Could you illustrate why a random walk process without a constant term exhibits stationarity in its first moment but not in the second?
Dimitru's user avatar
  • 177
3 votes
1 answer
196 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 ...
Mr. T's user avatar
  • 113
3 votes
1 answer
96 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} \...
Hyperbolic PDE friend's user avatar
3 votes
1 answer
367 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 $...
Michael Gmeiner's user avatar
3 votes
1 answer
3k views

HP Filter Smoothing Parameter

Mueller (2015, working paper) says that an HP filter with smoothing parameter 900,000 (for monthly data) corresponds to a smoothing parameter of 100,000 for quarterly data. How does one do this exact ...
FooBar's user avatar
  • 10.7k
3 votes
1 answer
563 views

Difference-in-differences with long time horizon and repeated treatments

I have a high-frequency panel dataset on the order of $i=150$ and $t=5000$. I am interested in studying the causal impact of a treatment with the following characteristics: The same unit can be ...
atkat12's user avatar
  • 133
3 votes
1 answer
100 views

Looking for discussion on equilibrium vs dynamic models in econometrics

I'm a statistician/machine learning scientist more familiar with molecular bio than economics. Trying to find out if an issue I perceive in bio modeling also occurs in econometric modeling. A common ...
Count Zero's user avatar
3 votes
1 answer
513 views

Replicate Romer and Romer (2004) results

I am trying to replicate figure 2 from Romer and Romer's (2004) paper on monetary shocks (http://eml.berkeley.edu/~dromer/papers/AER_September04.pdf). Essentially, having generated a series for ...
ts_highbury's user avatar
3 votes
2 answers
167 views

What is the reason why ARIMA(0,1,0) on $y_t$ and ARIMA(0,0,0) on diff($y_t$) are not identical time-series models?

I studied at BA level, that ARIMA(0,1,0) on $y_t$ and ARIMA(0,0,0) on diff($y_t$) are the same models. I am doing the Box–Jenkins model estimation on the historic data of US unemployment rate. My ...
Übel Yildmar's user avatar
3 votes
1 answer
158 views

Is 10 years monthly data enough for forecasting? [closed]

I want to forecast demand for the cement industry. I have data for 10 years- Monthly data. Is that desirable for forecasting?
Cha's user avatar
  • 31
3 votes
1 answer
781 views

Dealing with Missing Values in Diff-in-Diff Estimation

To preface this, I am asking this question on the Econ SE because I was made aware on Cross Validated that Difference in Difference estimation is quite an economics specific method. The picture above ...
fabla's user avatar
  • 141
3 votes
1 answer
101 views

If two variables are not cointegrated, can one still cause the other?

For part of a project, I wanted to see if electricity consumption causes GDP in Colorado. I initially intended to follow the approach of Mozumder and Marathe (2007), who use a VECM approach, but that ...
leecarvallo's user avatar
3 votes
1 answer
151 views

Show that the dividend price ratio is a ARMA(p, q) process

Let the log dividend growth evolve according to $\Delta d_{t+1} = \epsilon_{d, t+1}$ where $\epsilon_{d, t+1}$ is just white noise. Let the log returns be $r_{t+1} = x_t + y_t + \epsilon_{r, t+1}$ ...
elbarto's user avatar
  • 349
3 votes
1 answer
210 views

Regression - Testing for autocorrelation in the presence of heteroscedasticity

I have constructed a linear time series regression model and estimated the parameters by applying OLS. I now want to test wether the assumptions for proper large sample inference (asymptotic Gauß ...
shenflow's user avatar
  • 221
3 votes
1 answer
449 views

VECM interpretation in Matlab?

After testing for cointegration with Johansen test using the following code [h,pValue,stat,cValue,mles] = jcitest(ret,'model','H1*','lags',4,'display','params') ...
Adrian's user avatar
  • 41
3 votes
1 answer
75 views

Econometric test for detecting change from trend stationary to stationary process

I am stuck with the following problem from research. Is there an econometric test which detects change from trend stationary to stationary process. I tried to search for this but the literature is ...
anup's user avatar
  • 33
3 votes
1 answer
68 views

How can I write a conditional expectation of finite state markov process in matrix notation

NOTE: This question is related to the econometric method explored in the following two questions: Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/...
jmbejara's user avatar
  • 9,355
3 votes
1 answer
65 views

Can You Use Filtered Variables in OLS?

I have two variables that are non-stationary and contain stochastic trends. I used the Hamilton filter( an improvement over the HP filter) to remove the trend and isolate the cyclical component. My ...
user29937's user avatar
3 votes
1 answer
109 views

Does it matter which is the dependent variable in regression of time series data?

I am testing for cointegration between the Real GDP per capita of England and France. I use a Dickey-Fuller test to test for stationarity and concluded that both of my series are non-stationary. So I ...
Rumi's user avatar
  • 977
3 votes
2 answers
853 views

Examples of Covariance Stationary Time Series

I seem to be having trouble in comprehending what it means for a time series to be covariance stationary. Specifically, with the third condition that for any $t,h$ the $cov(x_t,x_{t+h})$ only depends ...
M. Damon 's user avatar

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