For this discussion I looked at the MU stock. Mu is the ticker for Micron Techonology, a manufacture of memory and storage products. It is a USA based technology supplier. We will only look at the closing price in the past 2 years.

Stock <- read.csv("../Downloads/Mu.csv") 

 stockprice <- ts(Stock[,5], start = decimal_date(as.Date("2018-10-24")), frequency = 252)

Stock price of MU from 2018 october to 2020 october. There is a general upward trend

Do not see seasonality in the stock price

Polar seasonal price also does not show seasonaility price change Using lag 1 shows more correlation 

 #using bias ajdusted forecast (forecast median)
 fc2 <- rwf(stockprice, drift=TRUE, lambda=0, h=30, level=80,
            biasadj=TRUE)
 res2 <- residuals(rwf(stockprice, drift=TRUE, lambda=0, h=30, level=80,
                      biasadj=TRUE))
  res3 <- residuals(forecast(stockprice, h=30))

Using the drift model and bias adjusted model we see an upward trend. However, the residual shows a sign of correlation and left skew. 

## 
##  Ljung-Box test
## 
## data:  Residuals from Random walk with drift
## Q* = 163.29, df = 100, p-value = 6.66e-05
## 
## Model df: 1.   Total lags used: 101

## 
##  Ljung-Box test
## 
## data:  Residuals from Random walk with drift
## Q* = 152.53, df = 100, p-value = 0.0005641
## 
## Model df: 1.   Total lags used: 101
 forecast(stockprice, h=30)
##          Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## 2020.815       52.19304 50.88693 53.49915 50.19552 54.19056
## 2020.819       51.17596 49.38020 52.97171 48.42958 53.92233
## 2020.823       50.65286 48.47488 52.83083 47.32193 53.98378
## 2020.827       51.11714 48.61466 53.61962 47.28993 54.94435
## 2020.831       52.34421 49.55472 55.13369 48.07805 56.61036
## 2020.835       54.10519 51.05559 57.15479 49.44123 58.76915
## 2020.839       53.71275 50.42354 57.00196 48.68234 58.74316
## 2020.843       52.97708 49.46457 56.48959 47.60516 58.34900
## 2020.847       53.24642 49.52398 56.96886 47.55344 58.93940
## 2020.851       53.16469 49.24354 57.08583 47.16781 59.16156
## 2020.855       52.41957 48.30931 56.52983 46.13347 58.70566
## 2020.859       52.04784 47.75680 56.33888 45.48526 58.61042
## 2020.863       50.88298 46.41846 55.34749 44.05509 57.71086
## 2020.867       51.30470 46.67321 55.93619 44.22145 58.38796
## 2020.870       51.81866 47.02600 56.61131 44.48893 59.14839
## 2020.874       52.77391 47.82534 57.72249 45.20573 60.34210
## 2020.878       51.88265 46.78292 56.98237 44.08329 59.68200
## 2020.882       50.04463 44.79811 55.29116 42.02076 58.06850
## 2020.886       49.64845 44.25912 55.03777 41.40618 57.89071
## 2020.890       49.90507 44.37663 55.43351 41.45005 58.36009
## 2020.894       50.71216 45.04801 56.37630 42.04960 59.37472
## 2020.898       50.36019 44.56353 56.15686 41.49496 59.22543
## 2020.902       51.26512 45.33890 57.19135 42.20174 60.32851
## 2020.906       51.75332 45.70031 57.80634 42.49603 61.01061
## 2020.910       50.75862 44.58142 56.93583 41.31141 60.20584
## 2020.914       50.46374 44.16480 56.76268 40.83034 60.09714
## 2020.918       51.69876 45.28039 58.11713 41.88271 61.51481
## 2020.922       50.26225 43.72663 56.79787 40.26689 60.25762
## 2020.926       51.28048 44.62967 57.93128 41.10895 61.45200
## 2020.930       49.32995 42.56593 56.09397 38.98528 59.67463

Using the forecast function above returns automatic ETS algorithm The residual plot shows no sign of correlation and normally distributed

## Warning in modeldf.default(object): Could not find appropriate degrees of
## freedom for this model.

```