Optimize 與 MASE

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1. load scipy.optimize.minimize

# weights are summed to be 1

2. cons = ({'type': 'eq', 'fun': lambda x:  1 - sum(x)})

3. def cal_mase(w):

       forecasts by w[0]*method0 + w[1]*mothod1 + ...

       calculate the mase from forecasts and testing set   

4. min_mase = minimize(cal_mase, init_weight0, method='SLSQP', constraints=cons)

5. get the weights

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wilcox.test

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How to estimate the parameters of ARIMA

https://stats.stackexchange.com/questions/77663/arima-estimation-by-hand

## Load Packages

library(stats)
library(forecast)

set.seed(456)


## Simulate Arima
y <- arima.sim(n=250,list(ar=0.3,ma=0.7),mean = 5)
plot(y)

## Optimize Log Liklihood for ARIMA

n = length(y) ## Count the number of Observatuions
e = rep(1,n) ## Initialize e

logl <- function(mx){

  g <- numeric
  mx <- matrix(mx,ncol=4)

  mu <- mx[,1] ## Constant Term
  sigma <- mx[,2] 
  rho <- mx[,3] ## Ar coeff
  theta <- mx[,4] ## Ma coeff

  e[1] = 0 ## Since e1 = 0

  for (t in (2 : n)){
    e[t] = y[t] - mu - rho*y[t-1] + theta*e[t-1]
  }

  ## Maximize Log Liklihood Function 
  g1 <-  (-((n)/2)*log(2*pi) - ((n)/2)*log(sigma^2+0.000000001) - (1/2)*(1/(sigma^2+0.000000001))*e%*%e)

  ##note: multiplying Log Likelihood by "-1" inorder to maximize in the optimziation
  ## This is done becuase Optim function in R can only minimize, "X"ing by -1 we can maximize
  ## also "+"ing by 0.000000001 sigma^2 to avoid divisible by 0
  g <- -1 * g1

  return(g)

}

## Optimize Log Liklihood
arimopt <- optim(par=c(10,0.6,0.3,0.5), fn=logl, gr = NULL,
                 method = c("L-BFGS-B"),control = list(), hessian = T)
arimopt

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Spyder profiler

need to be optimized