I have a dataset of the popularity of a certain word on the internet, and they are weekly counts from 2010-09-05 to 2015-09-27 and has an upward trend. I'm having a hard time identifying the model from its graphs, and I would love some help to interpret its ACF and PACF models. Thanks in advance!
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How do you estimate the appropriate forecast model for a time series by visual inspection of the ACF and PACF plots? Which one (i.e., ACF or PACF) tells the AR or the MA (or do they both)? Which part of the graphs tell you the seasonal and non-seasonal part for a seasonal ARIMA?  Consider the ACF and PCF functions displayed below.  They are from a log transformed series that's been differenced twice, one simple difference and one seasonal (, ).  How would you characterize the series? What model best fits it?
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Can anyone help me out with this question I found on my practice paper?  The series $\{y_t\}$ is described by $$ y_t = 5+0.3y_{t-1}+\epsilon_t+0.9\epsilon_{t-1}. $$ Identify the specific ARIMA model. What is the mean of the series $\{y_t\}$?  I think it is a ARMA (1,1) process? is that correct? And how do I calculate the mean of the ARMA model? Is it the same as AR model? If it is then $$ E(y_t) = 5/ (1-0.30) = 7.14?$$    The sample ACF and PACF plot of a series are given above. Appraise the patterns and judge which ARIMA model fit the series. Justify your conclusion.  I identified as the AR(4). Is that correct? Since ACF has an exponential decay and PACF has a cut off? Differencing is not needed as the ACF decreases sufficiently to 0.
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We can see who earned the most reputation in the current week, current month, current quarter, current year or all time. There is this  for that. Also see the below screenshot.    What struck me as odd was the different users for the Mathematics site. So I clicked on the picture that is listed as top user for the current year, which led me . Also see the below screenshot:    Here a different user is shown as the top user for 2019 when compared to the overall overview. I suspect the week or month listing to be somewhat volatile, but the difference between both users in this case is so big I can hardly blame caching.
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An interesting addition to the data dump would be the daily/hourly/whatever view counts for the websites. This could be used to see what happened to SO when proposal X came out, what time of day is the most active (if it was hourly), what day of the week is the most active, activity to question ratio, and many other things.   Before you say "What about Users.Views and Posts.ViewCount?", they aren't usable since they only list the total, not the breakdown of when it happened. The only statistics you could draw are monthly, which is useless.  If your worried about size, then your exaggerating what I'm asking. Daily is tiny, only 7 rows for an entire week. Hourly is a bit bigger, 168 rows per week. Considering other tables are millions of rows long, this won't affect size at all considering the growth.
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I started evaluating and comparing some methods in forecasting. I used Price of dozen eggs in US, 1900–1993, in constant dollars in the R software FMA package. I held out the last 10 years for assessment of forecast. Below are the results:  I used auto arima method in the R software. Obviously the results are way off. Am I doing something incorrect ? Below is the forecast. It does not recognize the declining trend.     I also used an unobserved components model (UCM) and obtained a good forecast,  as below.   Without outliers/level shifts there are very large standard errors and therefore wide confidence bands.  After some iterative work, below is the output with outliers/level shifts (I know I'm overfitting here) but it did a pretty good job in forecasting; there are also narrow confidence bands.    In looking at just this example the UCM seems to predict the hold-out sample more accurately than auto.arima.  Why is auto.arima not providing a reasonable forecast?  Are state space models/UCMs better for forecasting long range?  Are there any benefits of using one method over other?
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How are you dealing with the  in your machine learning models? Let's say you used to predict the number of sales each month. The virus affected your results last year and it will affect for at least a couple of months. So your model, I guess, is missing a lot. What are some approaches we can use to fix our models?
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I understand classification....a discrete response or category, like animal is dog or cat.  The author says..."Regression techniques predict continuous changes such as the change in temperature, power demand, or stock market prices."  I can't wrap my head around what he means.  Thanks.
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So for the last few months I've been doing a lot of forecasting for my company and specifically I've been looking at monthly forecasts of total weight of different categories of products output's each month.  I've been using time series models such as Arima, ETS, and tslm() within R to do my forecasting, as well as using cross validation to select a model. Over the last two days I've been presenting my results and discussing implementation of my forecasts.  But, I've been asked the same question multiple times and I don't know the answer to it, so let me ask you guys.  If this has been asked before, I apologize.  I'll write out a few questions that hopefully will make clear what I'm trying to understand.  Also, I'd like to keep technical answers about the models in the context of R, since that's what I'm using.   Do time series models take into account the number of days in a month? Particularly, do time series models consider the number of business days in a month? (or is there a way to incorporate this?) Do we even need to worry about this when forecasting using a time series model or does the model account for this?   For instance, lets say in October of 2014 a certain category sold 35,000 lbs of a product, and that there were 31 days, 23 of which were business days.  Well for this year, 2015, there are still 31 days, but now there are only 22 business days.  Just some background on the data, I have monthly data that starts in August of 2008.    So would it possibly be better to average the weight per month with the number of business days and forecast out this way since the # of business days change month to month and year to year?
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I am trying to prove/disprove that one time series is leading trend for the other ones. Two time series are (probably) independent and the movements are caused by some (let's assume unknown) common factors. What method would be most appropriate? I also want to find the leading period? Data is quarterly.
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Top is Poisson, bottom is Binomial Source of variation is different people observed over a week long period. 118 people to be exact.  want to make predictions about the proportion of days/week one exercises if they wake up at a given time.  &gt; summary(FMR7)  Call: glm(formula = No.Days.Ex ~ WaketimeStand, family = poisson, data = PSD)  Deviance Residuals:       Min        1Q    Median        3Q       Max   -2.99043  -0.64677  -0.03492   0.67393   1.51943    Coefficients:               Estimate Std. Error z value Pr(&gt;|z|)     (Intercept)    1.36991    0.04689  29.218   &lt;2e-16 *** WaketimeStand -0.08309    0.04806  -1.729   0.0839 .   --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for poisson family taken to be 1)      Null deviance: 124.55  on 115  degrees of freedom Residual deviance: 121.51  on 114  degrees of freedom AIC: 479.71  Number of Fisher Scoring iterations: 4  &gt; summary(FMR6)  Call: glm(formula = cbind(No.Days.Ex, No.Days.NotEx) ~ WaketimeStand,      family = quasibinomial(link = logit), data = PSD)  Deviance Residuals:      Min       1Q   Median       3Q      Max   -3.7483  -0.9585  -0.0625   1.0428   2.9739    Coefficients:               Estimate Std. Error t value Pr(&gt;|t|)   (Intercept)     0.2595     0.1009   2.571   0.0114 * WaketimeStand  -0.1869     0.1020  -1.832   0.0695 . --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for quasibinomial family taken to be 2.015388)      Null deviance: 288.42  on 115  degrees of freedom Residual deviance: 281.57  on 114  degrees of freedom AIC: NA  Number of Fisher Scoring iterations: 4  Quite clear that there is much more overdispersion on the quasibinomial than the poisson. The response variable is no.days exercise per week and so my original thought was to analyse with binomial GLM as it is the proportion of days in a week someone exercises. However, when modelled with a Poisson GLM it is much less overdispersed. Is this a sign I am using the wrong distribution.
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Can someone please tell me how the acf and pacf look like for a unit root process?
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I'm doing a textmining project about a videogame review dataset. I divided de reviews into a positive (reviewgrade > 8) and negative (reviewgrade &lt; 3) and want to draw conclusions based on the frequency of different grading factors mentioned in the text. I now have a dataframe with counts of certain categories mentioned per review.  0    13249 1     1565 2      292 3       65 4       19 5        6 6        4 7        3 8        2 9        1 Name: positive: gameplay, dtype: int64   0    5043 1     348 2      66 3      18 4       8 5       3 Name: negative: gameplay, dtype: int64   For example this are the distributions of the amount of reviews which have a certain amount of mentions of gameplay related words. There are for example 1565 reviews with precisely 1 mention of a word related to the category gameplay.  Now I want to use this data to determine if on average gameplay gets mentioned more in negative context than in positive or vice versa. Because the data is not normal distributed, I assumed a t-test is not appropriate, and found online that a Mann–Whitney U test might be suitable.  &gt; wilcox.test(positive$gameplay, negative$gameplay, alternative = "two.sided", conf.int = TRUE)      Wilcoxon rank sum test with continuity correction  data:  positive$gameplay and negative$gameplay W = 43702925, p-value &lt; 2.2e-16 alternative hypothesis: true location shift is not equal to 0 95 percent confidence interval:  2.963844e-05 4.797412e-05 sample estimates: difference in location            4.995671e-05    I do however get a very high W value, which doesn't seem to be correct. Is this not the appropriate test, or am I interpreting this wrong?
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I would like to understand why, under the OLS model, the RSS (residual sum of squares) is distributed $$\chi^2\cdot (n-p)$$ ($p$ being the number of parameters in the model, $n$ the number of observations).  I apologize for asking such a basic question, but I seem to not be able to find the answer online (or in my, more application oriented, textbooks).
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I am fitting an ARIMA model on a daily time series. Data are collected daily from 02-01-2010 to 30-07-2011 and are about newspaper sales. Since a weekly pattern in sales can be found (the daily average amount of copies sold is usually the same from Monday to Friday, then increases on Saturday and Sunday), I am trying to capture this "seasonality". Given the sales data "data", I create the time series as follows:  salests&lt;-ts(data,start=c(2010,1),frequency=365)   and then I use the auto.arima(.) function to select the best ARIMA model via AIC criterion. The result is always a non-seasonal ARIMA model, but if I try some SARIMAs model with the following syntax as example:  sarima1&lt;-arima(salests, order = c(2,1,2), seasonal = list(order = c(1, 0, 1), period = 7))   I can obtain better results. Is there anything wrongs in the ts command / arima specification? The weekly pattern is very strong so I would not expect so many difficulties in capturing it.  Any help would be very useful. Thank you, Giulia Deppieri  Update:  I have already changed some arguments. More precisely, the procedure selects ARIMA(4,1,3) as the best model when I set D=7, but AIC and the others good of fit indexes and forecasts as well) do not improve at all. I guess there's some mistakes due to confusion between seasonality and periodicity..?!   Auto.arima call used and output obtained:  modArima&lt;-auto.arima(salests,D=7,max.P = 5, max.Q = 5)     ARIMA(2,1,2) with drift         : 1e+20  ARIMA(0,1,0) with drift         : 5265.543  ARIMA(1,1,0) with drift         : 5182.772  ARIMA(0,1,1) with drift         : 1e+20  ARIMA(2,1,0) with drift         : 5137.279  ARIMA(2,1,1) with drift         : 1e+20  ARIMA(3,1,1) with drift         : 1e+20  ARIMA(2,1,0)                    : 5135.382  ARIMA(1,1,0)                    : 5180.817  ARIMA(3,1,0)                    : 5117.714  ARIMA(3,1,1)                    : 1e+20  ARIMA(4,1,1)                    : 5045.236  ARIMA(4,1,1) with drift         : 5040.53  ARIMA(5,1,1) with drift         : 1e+20  ARIMA(4,1,0) with drift         : 5112.614  ARIMA(4,1,2) with drift         : 4953.417  ARIMA(5,1,3) with drift         : 1e+20  ARIMA(4,1,2)                    : 4960.516  ARIMA(3,1,2) with drift         : 1e+20  ARIMA(5,1,2) with drift         : 1e+20  ARIMA(4,1,3) with drift         : 4868.669  ARIMA(5,1,4) with drift         : 1e+20  ARIMA(4,1,3)                    : 4870.92  ARIMA(3,1,3) with drift         : 1e+20  ARIMA(4,1,4) with drift         : 4874.095   Best model: ARIMA(4,1,3) with drift           So I assume the arima function should be used as:  bestOrder &lt;- cbind(modArima$arma[1],modArima$arma[5],modArima$arma[2]) sarima1&lt;-arima(salests, order = c(4,1,3))   with no seasonal component parameters and period specifications. Data and exploratory analysis show that the same weekly pattern can be approximatively considered for each week, with the only exception of August 2010 (when a consistent increase in sales is registered). Unfortunately I have no expertise in timeseries modeling at all, in fact I am trying this approach in order to find an alternative solution to other parametric e non-parametric models I have tried to fit for these problematic data. I have also many dependent numeric variables but they have shown low power in explaining the response variable: undoubtedly, the most difficult part to model is the time component. Moreover, the construction of dummy variables to represent months and weekdays turned out not to be a robust solution.
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acf(c(0,1,2,3,4,5),plot=FALSE) Autocorrelations of series ‘c(0, 1, 2, 3, 4, 5)’, by lag       0      1      2      3      4      5   1.000  0.500  0.057 -0.271 -0.429 -0.357    Why does the ACF output becomes negative as lag increases? My understanding is that no matter what the lag is, the series is in general increasing. Therefore the auto-correlation should be positive. For example, at lag 2, we are calculating the correlation function of the two series [0,1,2,3] and [2,3,4,5], where the positive correlation still holds. Where do I get this wrong?  Update  Here is my intuitive understanding of the acf of an monotonically increasing sequence:  ACF of a sequence is a function $\gamma(k)$ of the lag, k. By definition, this function indeed measures the correlation between $y_t$ and $y_{t-k}$. The misunderstanding comes from the understanding of correlation. A monotonically increasing sequence is not stationary, so the mean is not stable. In another word, the sequence does not exhibit mean reverting behavior. This distorts my usual understanding of correlation (when we think about the mean level at 0). Since the mean increases over time, those observations come earlier are more likely to be lower than the sample mean, thus inducing a negative sample acf when lag is larger.
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Following are acf and pacf plots of a monthly data series. The second plot is acf with ci.type='ma':    The persistence of high values in acf plot probably represent a long term positive trend. The question is if this represent seasonal variation?  I tried to see different sites on this topic but I am not sure if these plots show seasonality.           Edit: following is the graph for lag upto 60:     Following are plots of diff(my_series):     And upto lag 60:     Edit: This data is from:  Here the contributors did not consider acf and pacf plot of original or differenced series worth mentioning (so it must not be important). Only acf/pacf plots of residuals was referred to in a couple of places.
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I'm currently trying to apply a linear model (family = gaussian) to an indicator of biodiversity that cannot take values lower than zero, is zero-inflated and is continuous. Values range from 0 to a little over 0.25. As a consequence, there is quite an obvious pattern in the residuals of the model that I haven't managed to get rid of:   Does anyone have any ideas on how to solve this?