Skip to main content

New answers tagged

0 votes

Alternatives to Vector Autoregression

I'm a bit late to this party but depending on what you're trying to do, an OLS with time series errors model, or Vector Error Correction Models (VECMs) could work as an alternative to VAR if you're ...
Angela Helvin's user avatar
0 votes

GLMM with time-series covariance and binary response variable?

You can do this in the {mvgam} package, which fits dynamic regression models in State Space form for a fairly wide range of observation families. The ...
Nicholas Clark's user avatar
0 votes

Time series forecasting - Residuals not white noise

ARIMA is a linear model. It might be possible to explain some of these unusual variations in residuals by using non-linear models. I would have tried Machine Learning models on residuals to identify ...
Aaditya Bhardwaj's user avatar
1 vote

How to measure the strength of relationship

It is not obvious what is meant by "approx normal time series" in your question. Judging from the rest of it, it seems you meant that both your time series $x_t$ and $y_t$ follow a white ...
Mr. Ivan's user avatar
0 votes

Time series and separating variance by time scale

This sounds like a good candidate for a State-Space model, where you simultaneously model the underlying dynamics of the true process as well as the observation process. In State-Space models, both of ...
Nicholas Clark's user avatar
0 votes

Ecological modelling: multivariate abundance time-series data

For modeling integer-valued time series (or any non-Gaussian time series), I would opt for a State-Space model that allows the latent dynamic process to evolve independently of the observations. This ...
Nicholas Clark's user avatar
0 votes

How to forecast integer time series in R?

For modeling and forecasting integer-valued time series (or any non-Gaussian time series), I would opt for a State-Space model that allows the latent dynamic process to evolve independently of the ...
Nicholas Clark's user avatar
0 votes

Time Series of Wound Healing percentages / proportions

I agree this one is challenging, but you can design dynamic models that will respect the proportional nature and the temporal dependence of your observations. The {...
Nicholas Clark's user avatar
0 votes

Time series for count data, with counts < 20

For modeling integer-valued time series (or any non-Gaussian time series), I would opt for a State-Space model that allows the latent dynamic process to evolve independently of the observations. This ...
Nicholas Clark's user avatar
0 votes

How to fit a simple count time series INAR(1) model

For modeling integer-valued time series (or any non-Gaussian time series), I would opt for a State-Space model that allows the latent dynamic process to evolve independently of the observations. This ...
Nicholas Clark's user avatar
1 vote
Accepted

How to split and sample "Panel Data" when training a Logistic Regression to predict future outcomes

Best Practice for Splitting Panel Data For splitting panel data, the following approaches are often considered best practices: Temporal Validation (Out-of-Time) This involves setting aside data from ...
Esben Eickhardt's user avatar
0 votes

Long-term variance of AR(p)

UPDATE: I think I've figured it out. The Yule-Walker equations are the correct ones. When I was opening the expression of variance I was considering that $V[A+B] = V[A] + V[B]$. I was forgetting the ...
José Ivan's user avatar
0 votes
Accepted

Inferences with Filtered and Smoothed state estimates from a tracking problem

Ok so in my case the only solution I could come up with involved taking samples from the full posterior smoothing distribution. I'm not sure on the correct terminology here (this may be called Gibbs ...
Carlo Berger's user avatar
5 votes
Accepted

Compute R Squared by Fixing Betas for Multi Linear Regression without Intercept results in a large R Square

In OLS linear regression with an intercept, there are multiple equivalent expressions of $R^2$. Four come to mind. Squared Pearson correlation between the feature and the outcome Squared Pearson ...
Dave's user avatar
  • 63.7k
2 votes

Distribution of medians of triplicate samples taken from Gaussian distribution

Suppose $X_1, X_2, X_3 \text{ i.i.d. } \sim N(0, 1)$, then the density of the median $M := X_{(2)}$ is given by: \begin{align*} f_M(x) = 6\Phi(x)(1 - \Phi(x))\phi(x), \; x \in \mathbb{R}, \tag{1}\...
Zhanxiong's user avatar
  • 19.9k
5 votes

Distribution of medians of triplicate samples taken from Gaussian distribution

This must be known somewhere because Mathematica (and likely MATLAB and Maple, too) solves this easily. ...
JimB's user avatar
  • 3,889
0 votes

How to split and sample "Panel Data" when training a Logistic Regression to predict future outcomes

"There seems to be no consensus on what best practice is for splitting/sampling panel data". This is due to the fact that you may group these data in very different ways (e.g. by customer, ...
Ggjj11's user avatar
  • 1,343
1 vote

Regarding explosive AR processes and stationarity

changing an explosive AR process to be in a future dependent form is pointless, real life does not operate that way Is there a reason we don't consider the case of $|\phi|>1$? Is it also because &...
ABCBAA's user avatar
  • 73
2 votes

Brockwell/Davis seem to say more persistence implies better predictability---do I have a counterexample?

As things stand, I cannot see how the prediction MSE for any process that regularly has an error term $\epsilon_t$ with variance $\sigma^2$ coming in, independently of what happened before, can ever ...
Christian Hennig's user avatar
2 votes

timeseries model choose LSTM VS ARIMA

ARIMA forecasts numerical values. You could use it to forecast the student's future grades separately (and it would likely not work very well), but it will not help you in classifying a student as to ...
Stephan Kolassa's user avatar
0 votes

Forecasting positive time series with missing values and few observations

I would suggest you start with a State-Space model that allows for latent temporal processes to evolve through time, irrespective of whether or not observations occurred in that timepoint. This kind ...
Nicholas Clark's user avatar
2 votes
Accepted

How to detect a plateau at the end of a short time series?

I would use a Generalized Additive Model (GAM) to tackle this question. The penalized splines fitted with GAMs will be less likely to overfit than your LOESS algorithm, and you can use hierarchical ...
Nicholas Clark's user avatar
2 votes

Visualising complex data with various groups + sub-groups over time period

A tangent suggestion since this thread has come to the top... Ordering groups alphabetically is rarely meaningful for plotting. If a better ordering doesn't exist, as may be the case for names of ...
dariober's user avatar
  • 4,549
1 vote
Accepted

Synthetic Control - difference in data regarding the frequency

I am going to interpret "best" in terms of using the level of aggregation for the predictors that optimizes your ability to track the trajectory of the outcome variable for the treated unit ...
dimitriy's user avatar
  • 35.9k
0 votes

Are stationary processes non-predictable, and non-stationary ones predictable?

Here is a possible angle on this (cf. Brockwell/Davis, p40): The best linear predictor $l(Y_{T})=aY_{T}+b$ for a stationary time series $Y_{T+h}$ based on $Y_{T}$ minimizes $E[Y_{T+h}-aY_T-b]^2$ and ...
Christoph Hanck's user avatar
1 vote

Different time trends of groups: quadratic vs. linear decline

If you know/want to assume a priori that group A and group B follow time trends with different functional forms, you can hack it by using a dummy variable/indicator variable for each group. You can ...
Ben Bolker's user avatar
0 votes

Mixed model: Which parameters to provide for sample size calculations?

It seems you are trying to achieve three things here: Fit a multilevel model. Employ multiple DVs in said model. Estimate the statistical power of this model. Sointu's points are indeed useful for ...
Shawn Hemelstrand's user avatar
2 votes

Mixed model: Which parameters to provide for sample size calculations?

Yeah, the simr package is very good for power analysis for a multilevel model. Generally, you generate a mock dataset with your ID and time variables and all ...
Sointu's user avatar
  • 2,258
1 vote

Does time series with constant mean and constant variance implies weak stationary?

The requirement for weak stationarity are: $\mu_X(i) = \mathbb{E}[X_i] = \mu \text{ is independent of } i$, $\text{Cov}(X_{i+j}, X_i) = \mathbb{E}[(X_{i+j} - \mu_X(i + j))(X_i - \mu_X(i)] \text{ is ...
Rodion Raskolnikow's user avatar
4 votes
Accepted

How is mean-reversion behavior captured within ARIMA models? What coefficients determine speed of mean-reversion?

Let $\hat x_t=E(x_t\mid x_1,\dots,x_p)$ denote the expectation of $x_t$ conditional $x_1,x_2,\dots,x_p$. I leave it as an exercise to show that $\hat x_t$, for $t>p+q$, satisfies the homogeneous ...
Jarle Tufto's user avatar
  • 11.2k
2 votes

Convergence of predictions of an autoregressive model

Autoregressive model you are testing generates outputs by taking linear combinations of the last two observations in the sequence. Such a model can be represented with the Linear State Space ...
Han's user avatar
  • 121
4 votes

How is mean-reversion behavior captured within ARIMA models? What coefficients determine speed of mean-reversion?

Assuming the AR(p) $$ X_t = \mu + \phi_1 X_{t-1} + \phi_2 X_{t-2} + \ldots + \phi_{p} X _{t-p} + \epsilon_t.$$ is specified correctly, (i.e: invertible and $y_t$ is stationary ), then the long term ...
mlofton's user avatar
  • 2,507
0 votes

What properties must be verified for a simple OLS regression model with time series?

It seems that there is already an answer on Cross-Validated that answers (partially) my question: Using non-stationary time series data in OLS regression. To obtain useful results you can't use ...
Johannes Konrad's user avatar

Top 50 recent answers are included