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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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53 views

Simplest explanation of “Why isn’t an asset that produces recurring reliable dividends worth infinite money?”

Let’s say there exists an asset that is known to produce $1 of liquid value annually, indefinitely. In practice, this asset is worth a finite amount of money. However, to a naive intuition one could ...
0 votes
1 answer
16 views

Why given real and manually deflated series are not same in FRED?

when I deflate a series (for specific example, take M1 (M1SL) series from FRED) by CPI, it is not exactly the same as the one the that FRED provides i.e. M1REAL. It seems like M1REAL is a scaled up ...
1 vote
1 answer
37 views

Analysis of seasonal adjustments and moving averages: seeking guidance

I'm looking to seasonally adjust the price data I have using a moving average with a 12-month window size. As window 12 is being used, the first 11 values in the 'Oil_adjusted' column are being filled ...
0 votes
0 answers
25 views

Good practice in time series tests with different start/end dates

I am testing purchasing power parity on monthly data, in a sample of about 70 to 200 countries depending on which price index / currency pair is used. Would it be considered bad practice to use ...
0 votes
0 answers
38 views

How to interpret detrended data in GDP modelling?

So I detrend 5 variables that I fit in an Almon model to predict GDP. The problem is beforehand I detrend them and their values become much smaller. Also, I detrend the GDP itself and it becomes ...
0 votes
2 answers
100 views

Why is GDP a random variable?

I have seen in time series models that GDP is considered a random variable. At first, I found this troubling because I could not see any random process underlying the measurement. However, the ...
0 votes
0 answers
31 views

How to Find the Relationship Between Variables in Time-Series Data?

I would like to find the relationship between two variables (spending and earning) in time-series data and I am wondering if VAR would be a good way to approach this? If not, which approach(es) would ...
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0 answers
31 views

What should I do before an OLS regression and Johansen cointegration test with time series data?

I have to make a regression with real exports as the dependent and then an aggregated GDP income variable and the real effective exchange rate as independent variables. My variables are time series (...
2 votes
0 answers
31 views

What kind of econometric analysis can be used on Indian domestic petroleum sales 2008-2018? [closed]

I have data for sales of petroleum products across different states in India of both public sector and private sector companies for 10 years. Number of years: 2008 to 2018 monthly data (10 years) ...
0 votes
1 answer
79 views

How to assess the quality of a forecast?

Let's say I have a time series model (VAR model for example). How can I know that my forecast is good ? I could use the R2 but is there something else? I also know I could just use in sample ...
1 vote
0 answers
45 views

Help with Simulating a Time Series Process in R

I'm having difficulty expressing the following process in its most reduced form. Every time I try to simulate it with the arima.sim function, I end up with a non-stationary AR part that cannot be ...
2 votes
1 answer
127 views

Data analysis with GARCH modeling

I'm currently analyzing the relationship between stock, bonds, and real estate returns in Germany. I've gathered my data and am planning on estimating this equation: $\sigma_t = \beta_0 + \beta_1 R_{...
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?
2 votes
2 answers
647 views

Dickey Fuller Test

Consider the following AR(1) model: \begin{equation} Y_t = \alpha + \phi Y_{t-1} + \varepsilon_t \end{equation} I want to test the existence of a unit root for $Y_t$, and thus, I intend to implement a ...
0 votes
1 answer
55 views

Self-selection problem can be solved in panel data analysis?

Assume that there are two variables $x$ and $y$ and they both have trend. For example, (case 1) During covid-19, government spending($x$) and inflation($y$) are both increased (case 2) A productive ...
1 vote
0 answers
10 views

Normalization for model comparisons

I have a time series applying the Markov Switching model, which is estimated in about 15 different versions. One or two of the time series had to be normalized in order to converge. That is 1-2 out of ...
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0 answers
55 views

Forecasting and Structural Breaks

Let's say I am using walkforward evaluation for forecasting a certain time series with ARIMA and I want to test for structural breaks. And then I detect structural breaks. How can I use this ...
1 vote
0 answers
7 views

Is there a good catalogue of time serries available from the Federal government?

I have two closely related questions that I will present here in separate postings. It seems that lately I have spent a great deal of time looking for particular time series that may or may not exist. ...
1 vote
1 answer
92 views

Granger-Sims causality and subtle differences

For a bivariate process $(\textbf{X},\textbf{Y})=( (X_t, Y_t)^\top, t\in\mathbb{Z})$, we say that the process $\textbf{X}$ Sims-causes the process $\textbf{Y}$ (notation $\textbf{X}\overset{Sims}{\to}...
0 votes
0 answers
17 views

Separating VAR results by value of dummy variable

Suppose I have a dataset of this form: it is a time series dataset with some variables $y^1_t$ to $y^n_t$, and some dummy variables $d^1_t$ to $d^m_t$. Suppose I make a VAR model where the variables $...
0 votes
0 answers
18 views

MSVAR with predetermined regimes

Suppose I have a VAR model that relates income, consumption and investment. And suppose I want the parameters to vary by the political party in power: A, B or C. As far as I know, Markov Switching VAR ...
0 votes
0 answers
18 views

can i use a variable for ardl testing

i have done unit root testing on my time series variable using both the adf and pp test. at level difference my variables all appeared non stationary.i used the option 'trend' and speratley 'drift' on ...
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 ...
0 votes
1 answer
37 views

How to formulate intra-day return?

So I have time series data on the bitcoin price. For each day there is an open price and a close price. In many papers they calculae the return like this: $$ R_t = \Delta P / P_{t-1} = ln(P_t/P_{t-1})...
1 vote
1 answer
171 views

Critical Value for Chow Test

What are the degrees of freedom for the F-distribution used to find critical values for the Chow Test?
1 vote
0 answers
35 views

Does discount rate and cost of capital mean the same thing to compute levelised cost of energy (LCOE)?

I came to understand that cost of capital and discount rate are two different parameters, although they are also used ...
0 votes
0 answers
51 views

OLS estimation of AR and BLUE

Is it valid to apply OLS to the AR process?I learn that there exist correlation between explanatory variables and error term in AR model. I'm wondering how can show that $E(u_t|1,y_1,y_2,...,y_{t-1})\...
2 votes
1 answer
51 views

Which sample size would be best to investigate effects of War in Ukraine on volatility of stock prices using GARCH models?

I am planning to investigate the effect of the war in Ukraine on the stock market prices by including in a GARCH model a dummy identifying the burst of the war. I am wondering if I should strictly use ...
0 votes
0 answers
33 views

Running vector autoregressions with non-stationary data

I am reading Diego Kaenzig "The Macroeconomic Effects of Oil Supply News: Evidence from OPEC Announcements". I have a question about the baseline specification and in particular the ...
0 votes
1 answer
82 views

confidence interval for standard deviation of bitcoin price

I am actually doing some research on bitcoin for my bachelor thesis. I have daily data on the price of bitcoin from here. I calculated with python: ...
0 votes
0 answers
21 views

Ex post predictability of "mps" in Bauer, Swanson (2022)

I am reading the paper "A Reassessment of Monetary Policy Surprises and High-Frequency Identification" by Bauer and Swanson (2022). In Section 2, there is a Bayesian updating model that goes ...
2 votes
0 answers
161 views

How do I set up a staggered difference-in-differences design in R?

I have data which looks like this: ...
2 votes
0 answers
87 views

Regression OLS estimator with $x_t=1/t$

I found some questions in a book and wanted to train for my upcoming exam (expect to see some more posts from me idk), anyhow this is the question. To solve point A I rewrote the whole equation in ...
2 votes
1 answer
78 views

Why don't Time Series books talk about exogeneity like in classical linear regression models?

Consider the following linear regression: $$y_t = \beta_0 + \beta_1 x_{t} + u_t$$ Typically, we need to assume (assuming a random sample): \begin{equation}\label{I}\tag{I} E[u_t]=0, \quad cov(u_t ,x_t)...
2 votes
0 answers
60 views

Time series question from book (ma)

I'm trying to understand this subject and I'm stuck in a question found in a book. I understand white noise characterization, but I'm having some problems with this... maybe it's too much theory? I ...
2 votes
0 answers
47 views

Applications of a certain type of stochastic processes in macroeconomic, macroeconometric or finance

A compound Poisson random vector $Y$ is well defined in this site in wikipidia. Nothing prevents me from compound strictly stationary stochastic processes instead of compound random vectors. The ...
0 votes
2 answers
54 views

Comparison of two AR(1) regression models (lead in dependent vs lag in dependent variable)

What is the difference between these time series AR(1) regression models (lead in the dependent vs lag in the dependent variable)? $$\begin{align}y_t = constant + \alpha y_{t-1} + error \tag{1}\label{...
1 vote
2 answers
72 views

Include 'year' as an independent variable to deal with autocorrelation?

I'm working on an econometrics project for which I'm trying to study the impact of factors such as p.c. GDP growth, exports, inflation and interest rate on the debt-to-GDP ratio of a country, for 4 ...
1 vote
1 answer
34 views

The difference of a difference for a control variable in a regression?

I am conducting a time series analysis. My dependent variable is income inequality, which has been logged and then differenced. In other words, my Y variable is now the difference in log income ...
1 vote
1 answer
119 views

Machine learning and Inflation forecasting

Is machine learning a good tool to use in order to forecast inflation for the short term (next 2 - 3 years on a monthly or quarterly basis)? I want to be able to forecast inflation for Canada for the ...
1 vote
0 answers
55 views

Deriving ADF unit root test form for the time series with quadratic deterministic trend

I have the following time series process $y_t $ $$\Delta y_t = \delta + \gamma t + \epsilon_t$$ where $e_t$ is white noise process with the variance of $\sigma^2$. I guess that whereas $\Delta y_t$ is ...
0 votes
0 answers
147 views

Application of Maximum Likelihood estimation (MLE) to the Generalized Least Square (GLS) model

I have the following regression $$y = X\beta +u$$ where $y$ and $u$ are $(n\times 1)$ and $X$ is a fixed $(n \times k)$ matrix with full column rank and $\beta$ is an unknown $(k\times 1)$ vector of ...
1 vote
1 answer
34 views

The effect of stationarity of forecasting

If all that matters in forecasting is getting an accurate forecast then why is using non stationary data a problem. Say you use non stationary data to create a forecast that performs well in a pseudo ...
0 votes
1 answer
30 views

Which variable keep/get rid in a time series model?

Let s say I have a big VAR model with many variables. Then I run the model. How can I know which variables I should keep or get rid of if I want to ameliorate my model ? What if my model has so many ...
0 votes
0 answers
34 views

can someone help to interpret ACF and PACF graph?

can someone help to interpret ACF and PACF graph? in the graphs, I don't see any decay. am I right about that assumption other than that what can I comment about both? the data plotted is squared ...
1 vote
1 answer
178 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 ...
1 vote
0 answers
13 views

Is there granger causality that can be applied to panel data with structural breaks?

I have panel data containing various macroeconomic variables (for example: interest rate, output, unemployment). I would like to run a Granger causality test on some of them, but there are structural ...
2 votes
0 answers
48 views

A conceptual question about the limitation of the MA processes

We know that linear time-series techniques are frequently used in macroeconometrics. The Wold Representation Theorem states that any covariance-stationary process may be expressed as an MA process ...
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 $L=1$ ...
1 vote
0 answers
12 views

Time series: predicting covariates for missing years from historical values

I'm working with a time-series dataset where my dependent variable is measured annually from 2018-2021 but my covariates are not all measured over the same period. For instance, $x_1$ is measured from ...

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