Error In Time Series
be challenged and removed. (June 2016) (Learn how and when to remove this template message) In statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest. Since the forecast error is derived from the same scale of data, comparisons between the forecast errors of different series can only be made when the series are on the same scale.[1] In simple cases, a forecast is compared with an outcome at a single time-point and a summary of forecast errors is constructed over a collection of such time-points. Here the forecast may be assessed using the difference or using a proportional error. By convention, the error is defined using the value of the outcome minus the value of the forecast. In other cases, a forecast may consist of predicted values over a number of lead-times; in this case an assessment of forecast error may need to consider more general ways of assessing the match between the time-profiles of the forecast and the outcome. If a main application of the forecast is to predict when certain thresholds will be crossed, one possible way of assessing the forecast is to use the timing-error—the difference in time between when the outcome crosses the threshold and when the forecast does so. When there is interest in the maximum value being reached, assessment of forecasts can be done using any of: the difference of times of the peaks; the difference in the peak values in the forecast and outcome; the difference between the peak value of the outcome and the value forecast for that time point. Forecast error can be a calendar forecast error or a cross-sectional forecast error, when we want to summarize the forecast error over a group of units. If we observe the average forecast error for a time-series of forecasts for the same product or phenomenon, then we call this a calendar forecast error or time-series forecast error. If we observe this for multiple products for the same period, t
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(collected data) Data Mining Data Analysis Data Science Statistics (academic discipline)How does one interpret standard error in time series regression models?Inquiring about the standard error outputted by regression models. Is this the 'average' error? https://www.quora.com/How-does-one-interpret-standard-error-in-time-series-regression-models Can I expect with some probability that the actual result will be in https://www.researchgate.net/post/Are_there_any_methods_to_analyze_historic_error_of_time_series_to_improve_forecast_series the range of standard error (or multiple thereof) for future predictions? What is most commonly misunderstood about this metric?UpdateCancelAnswer Wiki3 Answers Daniel McLaury, [math]P[A \wedge B] \neq P[A] P[B][/math]Written 172w ago · Upvoted by Vladimir NovakovskiYou don't specify what kind of regression model you're talking about, so let's look at the simplest, which error in is linear regression with time on the X-axis. Linear regression fits your data to a model of the form[math]y = a t + \varepsilon[/math]where y is the time series, a is a coefficient, and [math]\varepsilon[/math] is a Gaussian random variable with mean zero and the specified variance. (In other words, we assume that the data comes from such a process, and given this assumption we calculate error in time which parameters give the "best fit" for our data.)If your data really comes from such a process -- if there's a fundamentally linear process relating the inputs to the outputs, with some (homoscedastic!) white noise thrown in at some step(s) along the way -- then linear regression will tell you the coefficients of that process and the volume of the noise. If it approximately comes from such a process, then you might get an approximate model. If your data doesn't come from this kind of model at all then you'll get numbers, too, but they won't mean anything.Okay, so let's assume that you're dealing with a process which is legitimately linear -- that your data is really generated by a process of the form[math]y = a t + \varepsilon[/math],where [math]\varepsilon \sim \mathcal{N}(0, \sigma^2)[/math]. When you actually run the regression, you're only giving it a finite sample, so it can't reliably determine the model parameters. Instead you'll get approximations [math]a_\ast[/math] and [math]\sigma_\ast[/math] -- for a model like the one above, given any data set whatsoever there's a (likely minuscule, but strictly nonzero) probability that it came from such a model, so strictly speaking you can't really rule anythi
analyze historic error of time series to improve forecast series? I want to improve the forecast using the historic error series. How can I do that? Please can anyone help me out? Topics Forecasting × 227 Questions 605 Followers Follow Statistical Analysis × 1,837 Questions 20,932 Followers Follow Statistical Data Analysis × 673 Questions 875 Followers Follow Time Series × 594 Questions 5,112 Followers Follow Nov 25, 2014 Share Facebook Twitter LinkedIn Google+ 2 / 0 Popular Answers Juehui Shi · University at Buffalo, The State University of New York Hi Durgaharish, From your further detailed explanation and question, I think the error you refer to is MAPE (Mean Absolute Percentage Error) or related, which is different from residuals in the model of regression analysis, because residuals are used to control model behavior be it linear, dynamic or stochastic. MAPE is one of the commonly applied measures or metrics for forecasting accuracy. Others include but not limited to ME (Mean Error), MSE (Mean Squared Error), RMSE (Root Mean Squared Error), MAE (Mean Absolute Error), MPE (Mean Percentage Error), Theil's U, Bias proportion UM, Regression proportion UR, and Disturbance proportion UD. Nov 29, 2014 Juehui Shi · University at Buffalo, The State University of New York Totally agree with Kaftan. He might call it error terms or better residuals. Seems that I guessed right at the first post. That is why I often use residuals. To improve forecasting accuracy in time series, you have to construct a model with the lowest criterion AIC, BIC, HQC. Also check for MAPE. Nov 27, 2014 All Answers (15) Juehui Shi · University at Buffalo, The State University of New York I do not quite understand the question. Do you mean the residuals of time series? If so, you have to follow Box-Jenkins approach to perform diagnostic checks on normality, autocorrelation (Ljung-Box Q test) and heteroskedasticity (correctable via G-ARCH). Forecasting accuracy can be measured by Mean Absolute Percentage Error (MAPE). Nov 25, 2014 Stefano Pisani · Italian Revenue Agency See Di Fonzo, Pisani, Savio in the book http://www.uni-mannheim.de/edz/pdf/eurostat/02/KS-AO-02-001-EN-N-EN.pdf Nov 25, 2014 Paul Louangrath · Bangkok University ISSUE: Forecast evaluation statistics via using error as the basis of analysis There may be an argument