Time series Definition and 49 Threads

Hello, I was under the impression that a time series with trend, seasonality, and cyclic component would automatically be nonstationary. Stationarity means constant mean, variance, and autocorrelation (weakly stationary). However, it seems that we could have a stationary time-series that has a...

Hello, I understand a few things about time series but I am unclear on other main concepts. Hope you can help me get on the right track. A time series is simply a 1D signal with the variable time ##t## on the horizontal axis and another variable of choice ##X## on the vertical axis. The time...

Hello everyone. I have a machine with a series of sensors. All sensors send a signal each minute. I want to know if any of those sensors are redundant. The data is available as an Excel file, where the columns are the variables and the rows are the measurements. I have 1000 rows. To do this, I...

I have an experimantally obtained time series: n_test(t) with about 5500 data points. Now I assume that this n_test(t) should follow the following equation: n(t) = n_max - (n_max - n_start)*exp(-t/tau). How can I find the values for n_start, n_max and tau so as to find the best fit to the...

Hi, I am not sure what the correct forum is for this question. Question: When do we need to remove seasonality from time series data to do a regression analysis? Context: I am planning to conduct a prediction analysis where I want to find out how a device performs. I hope to estimate a...

Hello, I'm trying to solve this, any idea please? Basically: Demonstrate for the next three processes if the Time Series would be stationary, if not, it should establish the conditions for it to be stationary. Thanks

Hi, I have some crucial questions belong to statistics: First, How can we derive the variance function with respect to mean for a given data? Secondly, I would like to ask: what method should we employ if the variance in time series behaves like a high order (such as ##𝑎𝑢_𝑡^5+𝑏𝑢_𝑡^4+𝑐𝑢_𝑡^3##...

Hey all, it's been awhile since done any calculus or DE's but was trying out some modelling (best price price per item for bulk value deals as a function of time and amount), in the last line i have f(n,t) implicitly. Any pointers or techniques for solving such things?

Hi, I am a beginner and I don't speak very well... So I'm really sorry for my poor scientific language... I work on 1-Dimension time series of a same system measured at different periods. In these periods, time series have different chaotic characteristics as their lyapunov exponent are...

I do a fair bit of spectral analysis of time series in my research, but to date my experience in the topic is almost exclusively from an engineering perspective rather than the more statistical approach. Of course I am aware that ultimately they are equivalent, but it means that my familiarity...

I have a time series model constructed by using ordinary least square (linear). I am supposed to provide some general comments on how one would improve the robustness of the analysis of a time series model (in general). Are there any general advice apart from expanding data, making it more...

Suppose we have monthly totals of observed data for last 35 years. That data is of inflow of a river in a reservoir and monthly demands from the reservoir. We are interested to check the effect of construction of a dam in the upstream. The effect is, whether the downstream reservoir will have...

If we can use Regression analysis to forecast, why do we use “Time Series Decomposition”? What's the difference between the 2? Thanks

I have some time series data of the absorbance of Br2 formation using UV Vis spectroscopy and I need to figure out the extinction coefficient/ absorptivity. The overall reaction is BrO3-+5Br- +6H+-->3Br2+3H2O which is expcted to go to completion I know that the equation relating absorbance to...

hi I have a random set of time series data that is calculated after applying an algorithm to a main random time serie data, and really need to extract all the possible characteristics from the set. The goal is to measure those characteristics and perform some statistical graphs based on those...

So I am studying chaotic dynamical systems and I need to find mutual information between two chaotic time series say x(t) and y(t). Any help would be much appreciated.

Hello Everyone, I will try to explain what am I doing here and I hope someone will understand. ACF - autocorrelation function I'm doing a research about non-parametric methods utility. How they fit and are useful in a different environment. I'm generating time series with different sizes of...

Homework Statement Calculate: PLIM (probability limit) \frac{1}{T} \sum^T_{t=2} u^2_t Y^2_{t-1} Homework Equations Y_t = \rho Y_{t-1} + u_t, t=1,...T, |\rho| <1 which the autoregressive process of order 1 E(u_t) = 0, Var(u_t) = \sigma^2 for t cov(u_j, u_s) = 0 for j \neq s The Attempt...

http://xkcd.com/1473/

$$\text{Consider the following decomposition of the time series }{Y}_{t}\text{ where }{Y}_{t}={m}_{t}+{\varepsilon}_{t},\text{ where }{\varepsilon}_{t}\text{ is a sequence of i.i.d }\left(0,{\sigma}^{2}\right)\text{ process. Compute the mean and variance of the process }{\nabla}_{2}{Y}_{t}\text{...

Not 100% sure if this is the right board. My question is to Show that a strictly stationary process with $E(X^2_t ) < ∞$ is weakly stationary. So weakly stationary implies two things: - the mean value function $u_t$ does not depend on time $t$ and - the autocovariance $\gamma_x(t+h,t)$ is...

I really need some help here, will appreciate any effort. I calculated time series of tidal stresses. It turned out that the probability of having positive tidal stress is 0.4 and negative - 0.6 (I counted up number of hours when the stress was positive/negative and divided by the total number...

hi I'm a physician and really need help from somebody who is good at probability. I calculated time series of tidal stresses. It turned out that the probability of having positive tidal stress is 0.45 and negative - 0.55 (I counted up number of hours when the stress was positive/negative and...

I am taking an introductory course in Time Series and our initial study of ARMA processes has proven to be challenging for me. The math we are asked to do is quite simple but recognizing various attributes is tricky. We are given 5 time series and are asked to label them from a given list of...

Hi there, Given a time series with data points x_1, x_2, x_3,...,x_n I want to be able to extrapolate its future behaviour. I can see three options: \sum_i (x_(i+1)-x_i)/x_i count of how many terms of (x_(i+1)-x_i) are positive and negative Assume linearity and calculate m for the best...

Author: James Douglas Hamilton Title: Time Series Analysis Amazon Link: https://www.amazon.com/dp/0691042896/?tag=pfamazon01-20

I wish it wasn't out of desperation that I'm making this first post! I have a neural network that is making predictions, the next 5 time points per training. Back testing consists of appending these 5 point sets together to produce a data set that spans time over a much longer period...

I'll be taking an introductory course on time series analysis in the spring, and we will be using the instructor's online notes as the "textbook". My previous experiences with such instructor's notes have been that they contain only the essentials of the course and aren't really useful as...

Hi I am an undergrad interested in learning time series analysis by himself. Other than the obvious prerequisite courses - 2nd year Calculus and Statistics - what else should I teach myself in prepreation for learning time series analysis? Thanks

I have a time series of climate data that I'm testing for stationarity. Based on previous research, I expect the model underlying the data to have an intercept term, a positive linear time trend, and some normally distributed error term. In other words, I expect the underlying model to look...

I'm choosing a database to write high-frequency time series data onto and have narrowed it down to MongoDB, Kyoto Cabinet or HDF5. I will be inserting 1200 rows of 8 entries per second, cumulating about 5 GB of data per day I'm estimating. Does anyone have experience between the three and...

I am trying to reproduce results of a paper. The model is: dS = (v-y-\lambda_1)Sdt + \sigma_1Sdz_1 \\ dy = (-\kappa y - \lambda_2)dt + \sigma_2 dz_2 \\ dv = a((\bar{v}-v)-\lambda_3)dt + \sigma_3 dz_3 \\ dz_1dz_2 = \rho_{12}dt \\ dz_1dz_3 = \rho_{13}dt \\ dz_2dz_3 = \rho_{23}dt \\...

Is correlation between 2 time-series a useful indicator? In currency pairs for example, sometimes the correlation between 2 pairs (e.g. EUR/USD and GBP/USD) for the past x days is strong, but it can weaken very fast. Should I just take the average over time and go with it, or is there a better...

Hello all, I am new to this forum and was wondering if any of you could help me out. I have this interview scheduled for next week for which I have to prepare a 10 min presentation on Uncertainty and how to determine it in a time series. Now, there is a wealth of information of the net...

I am trying to analyse a past series of numbers that flucuates between 107&210 with a normal frequency distribution of mean 162. What is the way to model and project short term future range for trendless but cyclical type of time series?

Homework Statement If I have a time series model x_1 = my + epsilon_1 x_i = my + a(x_{i-1} - my) + epsilon_i epsilon_i are iid standard normal. Can I then say that y = a_1 x_1+a_2 x_2 + ... a_n x_n is multi normal? The Attempt at a Solution All the x-es are normal...

Consider AR(1) process \(X_t=bX_{t-1}+e_t\) where \(e_t\) with mean of 0 and variance of \(\sigma^2\) and |b| <1 Let \( a_k \) be a recursive sequence with \( a_1 \) =1 and \( a_{k+1} = a_k + P_k +1\) for \( k = 1, 2 ,...,\) where \(P_k \) is Poisson iid r.v with mean = 1 also, assume \(P_t\)...

Consider an ARCH(1) model: Xt = σtZt, where Zt~ i.i.d. N(0,1) σt2 = w0 + w1 Xt-12 Find (i) E(Xt) and (ii) the autocovariance function γX(h) for h=0,1,2,3,..., assuming the process is second-order stationary. Solution: (i) E(Xt) = E[E(Xt|σt2)] =E[E(σtZt|σt2)] =E[σtE(Zt|σt2)] =...

Time Series: "Residuals" of ARMA model To check whether the white noise {at} are uncorrelated, we usually look at the residuals (which are sample estimates of the white noise {at}) and residual plots. But I just don't understand the meaning of "residuals" in the context of ARMA model...

Consider a stationary AR(2) process: Xt - Xt-1 + 0.3Xt-2 = 6 + at where {at} is white noise with mean 0 and variance 1. Find the partial autocorrelation function (PACF). I searched a number of time series textbooks, but all of them only described how to find the PACF for an ARMA process...

Theorem: A stationary AR(1) model can be expressed in terms of MA(infinity). Proof: Now I don't understand how they get from the second last line to the last line. Where did the term Yt-m go? I understand you can keep doing the substitution iteratively, but you always have to end...

Hi All, I've searched the web up and down, and a few textbooks, all to no avail. I have two time series (of 30 elements each), and I'd like to test if they are statistically different from each other (I suppose this could be reworded as, "are they equal" or "is their difference...

Hi, I have a question on stationarity in time series. I basically understand the concept, I think. However, I don't understand why the lag should affect the joint distribution. For example, the joint distribution of <Yt, Yt+a> should be the same as the joint distribution of <Yp...

Hi, I have a question regarding Fourier Series. I have a random set of time series data. Is there anyway to break this down into sines and cosines. From the literature I have read it seems like you can break down a function into sines and cosines but I need to do this for a random set of...

This post may seem a bit meandering, but it does well to fully communicate my thoughts and ultimate questions. Very little of the literature on Time Series Models makes reference to what is sparsely referred to elsewhere as the "Coefficient of Error", or even R-squared/Adjusted R-squared...

Hi all. Anyone can say to me as I can know if a time serie is in stationary regime?. I.E. What mathematical tool I must use to find out this when the time series is empirical? Thantks Horacio.

Hi, I am currently investigating environmental time series and algorithms to determine when an 'unexpected' event/reading has occurred in the series. I am currently constructing the gaussian probability density function (pdf) based on historical readings and checking if 'new' readings are...

Given a time series Yt, how can you decide what distribution the values obey, if any? In particular, is there a way to make sure the time series obeys a Gaussian distribution? Thanks, Frank

Analysis by Its History E. Hairer & G. Wanner Published by Springer, as part of their Undergraduate Texts in Mathematics series. ISBN 0-387-94551-2 http://www.springer-ny.com Introduction: For many first year Mathematics undergraduates an introduction to Analysis is often...