All Questions
Tagged with estimators time-series
23
questions
2
votes
1
answer
62
views
variance of the estimator of unconditional mean of AR(1) process
AR(1) process is defined as: $y_t=c+\phi y_{t-1}+\varepsilon_t$ where $\varepsilon_t$ is IID with mean zero and variance $\sigma^2<\infty$. For a stationary process, i.e. $\phi\ne 0$, the ...
- 61.8k
0
votes
1
answer
76
views
Unable to estimate AR(p) coefficients and $\sigma^2$
I am currently trying to solve this problem pertaining to the Yule-Walker equations:
Let $\{X_t\}_{t\in Z}$ be a causal autoregressive process given by $$X_t = \varphi X_{t−2} +W_t$$ with $\{W_t\}_{t\...
1
vote
1
answer
32
views
Generating "surrogate data" to calculate error on estimators
We have a dataset in the form of a time series $Y_n$.
We assume it follows an underlying parametric distribution $f(n,\beta)$, $\beta$ being the parameters.
From the observed dataset, we get an ...
- 113
4
votes
1
answer
641
views
Parameter estimation of state-space models with hidden variables
I have a time-series analysis problem, that I am having trouble finding a suitable regression technique for.
I have a coupled linear three dimensional system
\begin{align*}
X_{t} & =\left(1+J\...
- 41
2
votes
1
answer
49
views
What is this type of data called?
An event occurs once per period, such as once per year. Time is measured in discrete units, such as days of the year. Let $A_y$ be the day in year $y$ on which this event occurs. However, we do not ...
- 1,251
0
votes
1
answer
100
views
Estimating a statistic by combining two different data sources
Say you want to estimate a statistic $\theta$ and have two data sources. A sample from data source A can be treated as a low-variance, somewhat biased estimate of $\theta$. A sample from data source B ...
- 133
0
votes
0
answers
20
views
NN for resource management of an VM
Are there any papers/projects that deal with neural networks learning/adaptation for resource management (learning of system behavior and resource adaptation such as memory, CPU for an VM)?
e.g. some ...
- 316
1
vote
0
answers
25
views
Negatively correlated estimators for the AR-1 process
I have the following question. Assume we have a stochastic process
\begin{equation}
y_t = \gamma + \phi y_{t-1} + \epsilon_t, \ \epsilon_t \sim \mathcal{N}(0, \sigma^2),
\end{equation}
where $|\phi| &...
- 156
1
vote
0
answers
73
views
Moving estimators for nonstationary time series, like loglikelihood: l_T=sum_{t<T} a^{t-T} ln(rho(x_t))?
While in standard ("static") e.g. ML estimation we assume that all values are from a distribution of the same parameters, in practice we often have nonstationary time series: in which these parameters ...
- 421
3
votes
1
answer
1k
views
Is it possible to scale the mean and std of estimated rate/period, to another period?
Hello, all. When it comes to calculating the average from some time-spanning date, let's say the average of 20 weekly sales records from a specific store - while also calculating the standard ...
- 662
0
votes
1
answer
178
views
Proof for how the drift estimator, for a random walk with drift, is unbiased?
Random walk with drift formula is:
(Yt = α + Yt-1 + εt )
How do I go about checking that the drift estimator α-hat is unbiased.. which is proving that E(α-hat) = α?
Is this something I would need ...
- 13
2
votes
0
answers
73
views
Best way to estimate the probabilities of a random variable
I have some confusion about estimating the probability of a particular value of a random variable. For simplicity, consider the case of a coin and the random variable being $X = \{H,T\}$, where $T$ is ...
- 161
5
votes
1
answer
377
views
Derivation of the distribution of $\hat{\phi}=[\hat{\phi}_1, \cdots, \hat{\phi}_p]$ in AR(p) models
Background
Consider the following AR($p$) model:
$$
\dot{X_t} = \phi_1 \dot X_{t-1} + \phi_2 \dot X_{t-2} + \cdots + \phi_p \dot X_{t-p} + \epsilon
$$
where $\dot{X} := X - \mu = X - \mathbb{E}(X)$, ...
- 1,553
1
vote
0
answers
1k
views
Spherical error variance in OLS estimation of AR($p$)
Consider the linear model $\boldsymbol y=\boldsymbol X\beta+\boldsymbol\varepsilon$. One of the assumptions for the OLS estimator is the spherical error variance assumption which states that $\...
- 309
2
votes
0
answers
41
views
Conceptual questions on efficient estimators for MA model
I am trying to estimate parameters of a MA(p) system where p is the order. E.g.,
$$y[n] = \sum_{i=1}^p {\theta}_i u[n-i] + e[n] = \mathbf{\theta}^T\mathbf{u}[n] + ...
- 1,475