Questions tagged [time-series]

This tag is used for question related to time series models such as AR, ARMA, ARCH, GARCH and their properties and techniques used for inference.

A time-series model is one which postulates a relationship amongst a num- ber of temporal sequences or time series. An example is provided by the simple regression model

$$y(t) = x(t) \beta + \epsilon(t)$$

or more commonly,

$$y(t) = \sum_{i=1}^p \phi_i y(t-i)+ \sum_{i=1}^k \beta_i y(t-i)+\sum_{i=1}^q \mu_i \epsilon(t-i)$$

965 questions
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ACF of a MA(2) process

Does the ACF of a MA(2) process or generally other MA(q) processes show signs of slow decay? I have difficulties in pairing ACF and PACF graphs to AR or MA realizations. Could anyone give me a short guidance?
Dreason94
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Is the squared iid process iid?

I wanted to know whether squared iid process is iid or not. I mean, e(t)~iid => e(t)^2~iid?? I think, the squared process is iid also by my intuition but I'm not sure. help me!!
Park
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Determine the mean and autocovariance function of xt, and state whether it is stationary

I'm trying to understand the process to answer this question. Let $w_t,$ for $t=0, \pm1, \pm2,...$ be a normal white noise process, and consider the series: $x_t=w_tw_{t-1}$ Determine the mean and autocovariance function of $x_t$, and state whether…
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Smoothish points in-between known points in a time series

I have a bad feeling this is a well explored field I should already know about, but Say you have some platonic data at given points ... at 13.0: 1000 at 14.0: 1152 at 15.0: 1000 at 16.0: 1200 ... (of course, the times needn't be regular,…
Fattie
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Quick Time Series Question

I have two time series which are somewhat correlated, and I am tasked with discovering if one of the time series "leads" the other. I am guessing this means that, if one time series moves in a certain way, the other time series will move that way,…
user545426
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Calculating the speed of the tip of the hour hand

I am totally confused on how to calculate this. The whole entire question is: A hour hand is 20cm long. The speed of the hour hand tip is ________m/s. No other info other than that. Anyone help?
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Sum of autocovariance for AR(1)

Let a autoregressive process $AR(1)$ given by $$X_t = \phi_1X_{t-1}+\epsilon_t$$ where $|\phi_1|<1$. I am trying to show that $$\sum_{k=-\infty}^\infty \gamma(k) = \frac{\sigma_\epsilon^2}{(1-\phi_1)^2}.$$ I understand the result of $$\gamma(k) =…
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How is the second-order difference equation derived?

I'm reading through some documentation on timeseries. The first-order difference for timeseries is given as: $y'_{t} = y_{t} - y_{t-1}$ The second-order difference for timeseries is given as: $y''_{t} = y_{t} - 2y_{t - 1} + y_{t - 2}$ How is the…
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Finding the ACF and PACF

Q: Find the autocorrelation function (ACF) and the partial autocorrelation function (PACF) of the following AR(2) process up to and including lag 3: I am trying to understand how to find the ACF and PACf of time series in general. Is there a general…
zee
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Representing the "surprisingness" or "acyclicness" of events given binary time-series

I might just be missing a term or a concept, as Googling things like "measure acyclic events" mostly brings up non-relevant results (like DAGs). I'd be happy to continue researching on my own given any pointer (words) in the right direction. Is…
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Time average of function having more than one frequencies

I have a function f(t), if this function has only one harmonic frequency then its time averaged can be calculated in straight forward manner. But suppose if it has two frequencies whose corresponding time period are $T_1$ and $T_2$, how will I…
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How to identify models for time series?

I have a time series sales data and I am trying to figure a model for decomposition the components, but I am not sure on what model to choose Additive or Multiplicative as the graph looks confusing. Is there way other than looking at the graph to…
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AR(1) Process - Time Series

Is the time series $X_t = Y_t - 0.8Y_{t-1}$ an AR(1) process if $Y_t$ is a white noise process? I am guessing that the answer is yes since the time series $X_t$ depends upon $Y_{t-1}$, i.e. only the first lag. Is this conclusion correct?
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Forecasting next 12 months based on previous data using R

I'm having trouble doing a forecast based on previous data. I have data that represents eight years worth of monthly data $(n=96)$, for number of sales. I want to forecast the next 12 months based on this data using an optimal linear forecast, and I…
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Simplification of a Time Series Process

I have a time series $\{X_t\} = Z_t + \lambda(Z_{t-1} + Z_{t-2} + ... )$, where $Z_t$ is a White Noise process. Let $\{Y_t\} = X_t - X_{t-1}$ How does $$\{Y_t\} = X_t - X_{t-1} = (Z_t + \lambda\sum_{j=1}^{\infty}Z_{t-j}) - (Z_{t-1} +…