library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

Load Data

Q <- read.csv("C:/Users/yiq00/OneDrive/Desktop/BC/QQQ.csv")
Q =ts(Q[,2],start=c(2018,10,29),end=c(2020,10,27),frequency=250)

Plot

plot.ts(Q)

then Take difference to remove the trend and create a timeplot

DQ = diff(Q)
plot.ts(DQ)

fit_ets = ets(DQ)
## Warning in ets(DQ): I can't handle data with frequency greater than 24.
## Seasonality will be ignored. Try stlf() if you need seasonal forecasts.
print(summary(fit_ets))
## ETS(A,N,N) 
## 
## Call:
##  ets(y = DQ) 
## 
##   Smoothing parameters:
##     alpha = 1e-04 
## 
##   Initial states:
##     l = 0.2305 
## 
##   sigma:  3.5702
## 
##      AIC     AICc      BIC 
## 4383.915 4383.964 4396.559 
## 
## Training set error measures:
##                       ME    RMSE      MAE  MPE MAPE      MASE       ACF1
## Training set 0.002649886 3.56303 2.437873 -Inf  Inf 0.6132582 -0.1141793
##                       ME    RMSE      MAE  MPE MAPE      MASE       ACF1
## Training set 0.002649886 3.56303 2.437873 -Inf  Inf 0.6132582 -0.1141793

Using this model to estimate

checkresiduals(fit_ets)

## 
##  Ljung-Box test
## 
## data:  Residuals from ETS(A,N,N)
## Q* = 83.171, df = 98, p-value = 0.8576
## 
## Model df: 2.   Total lags used: 100
FQ = forecast(fit_ets, h=1)
autoplot(FQ, include=24)

accuracy(FQ)
##                       ME    RMSE      MAE  MPE MAPE      MASE       ACF1
## Training set 0.002649886 3.56303 2.437873 -Inf  Inf 0.6132582 -0.1141793
print(summary(FQ))
## 
## Forecast method: ETS(A,N,N)
## 
## Model Information:
## ETS(A,N,N) 
## 
## Call:
##  ets(y = DQ) 
## 
##   Smoothing parameters:
##     alpha = 1e-04 
## 
##   Initial states:
##     l = 0.2305 
## 
##   sigma:  3.5702
## 
##      AIC     AICc      BIC 
## 4383.915 4383.964 4396.559 
## 
## Error measures:
##                       ME    RMSE      MAE  MPE MAPE      MASE       ACF1
## Training set 0.002649886 3.56303 2.437873 -Inf  Inf 0.6132582 -0.1141793
## 
## Forecasts:
##          Point Forecast     Lo 80    Hi 80     Lo 95    Hi 95
## 2020.040      0.2306205 -4.344746 4.805987 -6.766798 7.228039
##          Point Forecast     Lo 80    Hi 80     Lo 95    Hi 95
## 2020.040      0.2306205 -4.344746 4.805987 -6.766798 7.228039