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You don't need hacks, this can be tackled using vanilla Bayes theorem. The more informative your prior is, the more weight in has on the final result. The opposite is also true, the more information your data provides, so also the larger sample size, the more weight it has. So just have your priors to be more informative. To achieve this, you need priors ...
5
ARIMA and similar models assume some sort of causal relationship between past values and past errors and future values of the time series: $$Y_{t+h}=f(Y_{t},Y_{t-1},Y_{t-2},....,\epsilon_{t},\epsilon_{t-1},\epsilon_{t-2},...)$$ e.g. the volatility of a stock today is causally driven by the volatility of that stock yesterday and two days ago, the population ...
4
If you really don’t trust your likelihood, for example if your observations in reality violate an assumption of independence, you could down-weigh the likelihood. For example, you could raise the likelihood to a power of 1/2, which in effect would reduce the sample size by a factor of two. If instead up-weighing the prior as you propose, this would clearly ...
4
There is a difference between forecasting into the future (predicting $y_{t+1}$ based on $y_t$) and contemporaneous prediction (predicting $y_t$ based on $x_t$).
As discussed in the linked question, forecasting into the future necessarily involved lagged dependent variables in the regression. In this case, serial correlation in the residuals indicates serial ...
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+1 to Gordon's answer.
Forecast accuracy "guidance" or "benchmarks" are not worth the bits they take up. They are typically derived from surveys on a convenience sample. I went into some detail in a critique of such benchmarks in an article (Kolassa, 2008, Foresight: The International Journal of Applied Forecasting). Yes, it's a couple of ...
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Those Lewis numbers are fairly arbitrary, you cant just say that a 20% error is good forecasting because some guy wrote it in a book 40 years ago.
The acceptable margin or error completely depends on the problem domain. In some situations a model that gives a 20% error will be great, in others it will be unusable. I know its tempting to rely on general rules ...
3
Indeed, the procedure you describe is what it is typically done in mixed-effects models. When you fit the models under maximum-likelihood you only get $\hat \theta$, and then using empirical Bayes you get an estimate of $\hat b_i(\hat \theta)$, which you plug-in the equation to obtain a prediction for a particular subject. In the context of linear mixed ...
3
The reference page on the fable website contains an organised list of models: https://fable.tidyverts.org/reference/
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The most reliable way of understanding the capabilities of a package is, as always its CRAN page. In the specific case of the fable package, we find its reference manual and two different vignettes, one introduction and one vignette on forecasting with transformations.
The reference manual in particular looks helpful. For instance, I see no less than ten ...
2
Yes, summing daily forecasts to weeks is a common approach.
The alternative would be to base your model on weekly input data and directly forecast weekly totals. (If you have causal factors that change in mid-week, you will need to do some jiggling with the regression.)
Of course, the two forecasts - bottom-up and direct - will usually not give the same ...
2
A lot depends on the precise formulation of the null hypothesis you would like to test. You could formulate a hypothesis such as
$H_0\colon$ model $A$ and model $B$ have equal expected forecast loss for each of the 10 time series
against an alternative
$H_1\colon$ $H_0$ is not true
and test $H_0$ using a series of vanilla Diebold-Mariano tests with a ...
2
In practice of forecasting there's very little that is absolute. This is one such case where there is not prescribed course of actions. Presumably you started with a time series regression model $y_t=X_t\beta+\varepsilon_t$ where $\varepsilon_t\sim\mathcal N(0,\sigma^2)$.
Once you looked at residuals $\hat\varepsilon_t$ and noticed that they're autocorelated,...
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This is known as an ARMAX model. Note that this is different from what forecast::auto.arima() with external regressors provided in the xreg parameter fits, which is a regression with ARIMA errors. If you search for "ARMAX R", you need to be careful about the distinction between the two kinds of models, because this is very frequently confused. More ...
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Here is a working example for the extraction of the desired distributional components. Bear in mind that this is the distribution on a transformed scale. Maybe this link gives some more explanation on this topic:
Forecasting using transformations
library(tsibbledata)
library(tsibble)
library(dplyr)
#>
#> Attache Paket: 'dplyr'
#> The following ...
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The difference in the observed importance of some features when running the feature importance algorithm on Train and Test sets might indicate a tendency of the model to overfit using these features. This is indeed closely related to your intuition on the noise issue.
In other words, your model is over-tuned w.r.t features c,d,f,g,I.
Running feature ...
1
Because it is the best ARIMA fit for your data, there is likely no mistake.
The 63rd observation is indeed a big outlier. It is ~30 times bigger than standard deviation for other observations. Even if there was some autocorrelation structure in your data, you would often not be able to discern it with such outlier, so trying to remove it is a good approach.
...
1
library(forecast)
fit <- Arima(USAccDeaths, order=c(0,1,1), seasonal=c(0,1,1))
fit %>% forecast() %>% autoplot()
Created on 2020-06-23 by the reprex package (v0.3.0)
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Your choice of Prediction Interval (PI) width depends on what you plan on doing with the PI. For instance, if you will use it to set safety stocks, you can determine the optimal quantile, be it 80%, 90% or 95%. (In this case, you would usually not use both endpoints of the PI, but only the upper one.)
Using a "100% PI" often does not make a lot of ...
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There are multiple issues present.
The first one is that otm.arxiv() does not follow the standard R practice of returning a fitted model that one applies forecast() to. Instead, it performs fitting and forecasting. To obtain a forecast from otm.arxiv(), you need to supply an h parameter to it:
otm.arxiv(y,h=3,thetaList=seq(from=1,to=5,by=0.5),g="SE&...
1
I played with Prophet a bit. They promise big. As I understood their claim was for the framework for massive forecasting. If you have 10,000 series to forecast, there's no way to do it manually. So, let's just run the thing on all of them automatically, and maybe we'll get a decent set of forecast on average.
In finance we also forecast massive numbers of ...
1
Given your model, your forecast is reasonable whichever of the two ways you specify the external regressor (I think the two ways are equivalent; note that the true value of $\mu$ is defined relative to how you specify the external regressor). You just extrapolate the negative trend, having adjusted for the mean. The mean is high relative to the few preceding ...
1
"Missing values" is something different than "no orders". In the first case, we don't know whether there were orders or not, in the second case we know there were none. This makes a difference.
Your raw data are what is known as "lumpy" (many zeros, high non-zero values). This is even harder to forecast usefully than non-lumpy demands (many zeros, low non-...
1
Well you can, and this is often done in practice, do something like a MAPE with a hold out data set and see which works best, but there is no rule I know of if one predict some data sets better and the other predicts other data sets better. Nor is this a formal statistical test. You might consider how the various M contest have addressed this (I think they ...
1
I would say the quoted statement is ambiguous and possibly misleading.
Heteroskedasticity does not affect forecasting but serial correlation would
make point forecast invalid.
In general, forecast implications of residual diagnostics are:
No heteroskedasticity and no serial correlation
Forecast can be computed using consistent parameter estimates and ...
1
GARCH models the entire distribution of a time series with (potentially) time-varying mean, time-varying variance but constant distributional features otherwise (e.g. time-constant higher moments once time variation in the first two moments is accounted for). The distribution of $y_t$ modelled by GARCH is moving up and down due to the conditional mean ...
1
If you are interested in forecasting time series data you should follow Rob Hyndman and his blog https://robjhyndman.com/hyndsight/.
Start by reading his book Forecasting: Principles and Practice. You can find an online free version here https://otexts.com/fpp3/.
Then if you are interested in Financial data, I suggest you Rue Tsay Financial Time Series book,...
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What does "state of the order book" mean?
Besides the best bid and ask, what other information does your data contain? E.g. depth of the book? If so, how many levels?
How it "return" defined? Buy at the best ask and sell at the best bid two minutes later? At this granularity, price impact may matter. Depending on order size and size of the queue, you may ...
1
Do you think it is a good way to solve this problem or should I re-construct my architecture? I wonder if there are other proven ways for SKU level price optimization in an e-com scenario. Any ideas, inputs would be highly appreciated.
In theory, you can use an MLP for just about anything (thanks to the universal approximation theorem) so your approach is ...
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Croston method and its variants create a linear prediction. It only changes when demand occurs.
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The answer of rjt90 is correct but since I'm working on these models, I thought I expand on it.
Score-driven framework
In the class of score-driven models (or GAS models), the time-varying parameter $\alpha_t$ is updated over time using an autoregressive updating function based on the score of the conditional observation probability density function, see
...
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