Interview

Import Python libraries

#install.packages("reticulate")

library(reticulate)

install_python(version = '3.9.13')

+ '/Users/satoshi/Library/Application Support/r-reticulate/pyenv/bin/pyenv' update
+ '/Users/satoshi/Library/Application Support/r-reticulate/pyenv/bin/pyenv' install --skip-existing 3.9.13

[1] "/Users/satoshi/.pyenv/versions/3.9.13/bin/python3.9"

reticulate::repl_python()
print('hello world')

hello world

#!pip install pandas
import pandas as pd
import datetime


data = pd.read_csv('https://filtereddatasets.s3.amazonaws.com/Groceries_retail/Groceriesv2.csv')

data.columns

Index(['Order_no', 'Prod_no', 'Prod_name', 'Sale_date', 'Sale_time',
       'No_of_units', 'Unit_price', 'Total_amt'],
      dtype='object')

data = data.drop(['Order_no', 'Prod_no', 'Sale_time','No_of_units', 'Unit_price'], axis=1)

data['Sale_date'] = pd.to_datetime(data['Sale_date'])
data['Total_amt'] = data['Total_amt'].str.replace('$', '').astype(float)
data['Prod_name'] = data['Prod_name'].astype(str).str.strip()

data = data.groupby(['Sale_date', 'Prod_name'])['Total_amt'].sum().reset_index()

data.to_csv('prueba.csv')
data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 90138 entries, 0 to 90137
Data columns (total 3 columns):
 #   Column     Non-Null Count  Dtype         
---  ------     --------------  -----         
 0   Sale_date  90138 non-null  datetime64[ns]
 1   Prod_name  90138 non-null  object        
 2   Total_amt  90138 non-null  float64       
dtypes: datetime64[ns](1), float64(1), object(1)
memory usage: 2.1+ MB

Doing stuff in R

quit
library(fpp3)

── Attaching packages ────────────────────────────────────────────────────────────────────────────────────────────────────────────────── fpp3 0.5 ──
✔ tibble      3.2.1     ✔ tsibble     1.1.3
✔ dplyr       1.1.3     ✔ tsibbledata 0.4.1
✔ tidyr       1.3.0     ✔ feasts      0.3.1
✔ lubridate   1.9.2     ✔ fable       0.3.3
✔ ggplot2     3.4.3     ✔ fabletools  0.3.3
── Conflicts ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────── fpp3_conflicts ──
✖ lubridate::date()    masks base::date()
✖ dplyr::filter()      masks stats::filter()
✖ tsibble::intersect() masks base::intersect()
✖ tsibble::interval()  masks lubridate::interval()
✖ dplyr::lag()         masks stats::lag()
✖ tsibble::setdiff()   masks base::setdiff()
✖ tsibble::union()     masks base::union()

read.csv('prueba.csv') |>
  mutate(Date = ymd(Sale_date)) |>
  select(-Sale_date) |>
  as_tsibble(key = Prod_name, index = Date) |>
  select(Date, Prod_name, Total_amt) -> prueba_tsibble

prueba_tsibble

Summarize sales

# library(dplyr)
total_sales <- prueba_tsibble |>
  summarise(TOTAL = sum(Total_amt))

total_sales |> autoplot()

Plot variable not specified, automatically selected `.vars = TOTAL`

gg_season(total_sales, period = "week")

Plot variable not specified, automatically selected `y = TOTAL`

gg_subseries(total_sales, y=TOTAL, period = 'week') 

total_sales |>
  model(STL(TOTAL)) |>
  components() |>
  autoplot()

fit_total_sales <- total_sales |>
  model(TSLM(TOTAL ~ trend() + season()))

fc_total_sales <- forecast(fit_total_sales)
fc_total_sales |>
  autoplot(total_sales) +
  labs(
    title = "Forecasts of TOTAL sales using regression",
    y = "$"
  )

SEASONAL ARIMA

total_sales |>
  gg_tsdisplay(difference(TOTAL, 12),
               plot_type='partial', lag=36) +
  labs(title="Seasonally differenced", y="")

Differentiated

total_sales |>
  gg_tsdisplay(difference(TOTAL, 12) |> difference(),
               plot_type='partial', lag=36) +
  labs(title = "Double differenced", y="")

FITTING

install.packages("urca")

trying URL 'https://cran.rstudio.com/bin/macosx/big-sur-x86_64/contrib/4.3/urca_1.3-3.tgz'
Content type 'application/x-gzip' length 1106346 bytes (1.1 MB)
==================================================
downloaded 1.1 MB

The downloaded binary packages are in
    /var/folders/ly/0xqts46d0xb6mpwwrttmy0tc0000gq/T//RtmpA4Tod9/downloaded_packages

library(urca)

fit <- total_sales |>
  model(
    arima012011 = ARIMA(TOTAL), #~ pdq(0,1,2) + PDQ(0,1,1)),
    arima210011 = ARIMA(TOTAL), #~ pdq(2,1,0) + PDQ(0,1,1)),
    auto = ARIMA(TOTAL, stepwise = FALSE, approx = FALSE)
  )

Pivot

fit |> pivot_longer(everything(), names_to = "Model name",
                     values_to = "Orders")

Glance

glance(fit) |> arrange(AICc) |> select(.model:BIC)

Residuals best model

fit |> select(auto) |> gg_tsresiduals()

White noise residuals?

augment(fit) |>
  filter(.model == "auto") |>
  features(.innov, ljung_box)

Forecast

forecast(fit, h=36) |>
  filter(.model=='auto') |>
  autoplot(total_sales) +
  labs(title = "Total sales for Grocery Store",
       y="$")

Another Forecast

total_sales |>
  model(ARIMA(log(TOTAL) ~ 0 + pdq(3,1,1) + PDQ(2,1,2))) |>
  forecast() |>
  autoplot(total_sales) +
  labs(title = "Total sales for Grocery Store",
       y="$")

Neural

fit <- total_sales |>
  model(NNETAR(TOTAL))

fit

fit |>
  forecast(h = 14) |>
  autoplot(total_sales) +
  labs(y = "$", title = "Total Sales Forecast")

Forecasting 30 observations

fit2 <- total_sales |>
  model(NNETAR(sqrt(TOTAL)))

fit2

fit2 |>
  forecast(PI = TRUE, h = 5) |>
  autoplot(total_sales) +
  labs(y = "$", title = "Total Sales Forecast")

fit2 |>
  generate(times = 10, h = 30) |>
  autoplot(.sim) +
  autolayer(total_sales, TOTAL) +
  theme(legend.position = "none")

Another way to do it

# Generate forecasts
forecast_result <- forecast(fit2, h = 30, level = c(80, 95))

# Plot the original data
total_sales_plot <- autoplot(total_sales) +
  labs(y = "$", title = "Total Sales Forecast")

Plot variable not specified, automatically selected `.vars = TOTAL`

# Add forecast and prediction intervals to the plot
total_sales_plot +
  autolayer(forecast_result, series = "Point Forecast", PI = TRUE, fill = "blue") +
  guides(fill = guide_legend(title = "Prediction Intervals"))

Warning: Ignoring unknown parameters: `series` and `PI`Warning: Ignoring unknown parameters: `series` and `PI`Warning: Ignoring unknown parameters: `series` and `PI`Warning: Ignoring unknown parameters: `series` and `PI`

Prediction Intervals

library(forecast)

Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 

Attaching package: ‘forecast’

The following object is masked from ‘package:fabletools’:

    accuracy

set.seed(2015)
(fit <- nnetar(lynx, lambda=0.5))

Series: lynx 
Model:  NNAR(8,4) 
Call:   nnetar(y = lynx, lambda = 0.5)

Average of 20 networks, each of which is
a 8-4-1 network with 41 weights
options were - linear output units 

sigma^2 estimated as 95.77

sim <- ts(matrix(0, nrow=20, ncol=9), start=end(lynx)[1]+1)
for(i in seq(9))
  sim[,i] <- simulate(fit, nsim=20)

library(ggplot2)
autoplot(lynx) + forecast::autolayer(sim)

For a multivariate time series, specify a seriesname for each time series. Defaulting to column names.

Plot

fcast <- forecast(fit, PI=TRUE, h=20)
autoplot(fcast)

Chainging the Data

library(forecast)
set.seed(2015)
(fit_with_intervals <- nnetar(y=total_sales$TOTAL, lambda=0.5))

Series: total_sales$TOTAL 
Model:  NNAR(20,10) 
Call:   nnetar(y = total_sales$TOTAL, lambda = 0.5)

Average of 20 networks, each of which is
a 20-10-1 network with 221 weights
options were - linear output units 

sigma^2 estimated as 19.91

total_sales

SIMULATION

# Create a time series with a proper date index
start_date <- as.Date("2018-01-011")  # Change this to your actual start date
sim <- ts(matrix(0, nrow=30, ncol=30), start=start_date)

# Generate simulated data for the time series
for(i in seq(30))
  sim[,i] <- simulate(fit_with_intervals, nsim=30)

library(ggplot2)
library(forecast)

# Create a date index for the time series
date_index <- seq(start_date, by = "days", length.out = 30)
date_index

 [1] "2018-01-01" "2018-01-02" "2018-01-03" "2018-01-04" "2018-01-05" "2018-01-06" "2018-01-07" "2018-01-08" "2018-01-09" "2018-01-10" "2018-01-11"
[12] "2018-01-12" "2018-01-13" "2018-01-14" "2018-01-15" "2018-01-16" "2018-01-17" "2018-01-18" "2018-01-19" "2018-01-20" "2018-01-21" "2018-01-22"
[23] "2018-01-23" "2018-01-24" "2018-01-25" "2018-01-26" "2018-01-27" "2018-01-28" "2018-01-29" "2018-01-30"

# Create a date index for the time series
date_index <- seq(start_date, by = "days", length.out = 30)
# Assign the date index to the time series
time_series <- ts(sim, start = start_date)
time_series

Time Series:
Start = 17532 
End = 17561 
Frequency = 1 
      Series 1 Series 2 Series 3 Series 4 Series 5 Series 6 Series 7 Series 8 Series 9 Series 10 Series 11 Series 12 Series 13 Series 14 Series 15
17532 47008.53 48286.88 48066.66 48608.81 48561.26 48087.91 47369.64 49408.28 47465.35  48369.16  47835.77  48127.05  47334.12  48054.57  48252.92
17533 53028.08 55505.28 54158.44 54428.32 55521.80 55926.85 54152.50 56132.58 54242.52  56720.68  55877.15  55328.20  55930.74  57239.13  55877.04
17534 46568.63 45360.90 46258.53 45416.19 44865.66 43061.42 44393.99 44958.75 43607.29  46054.74  45643.07  44709.48  44838.54  45990.35  45853.08
17535 52603.96 53324.93 53049.46 54809.50 53203.58 51483.29 53260.50 55019.17 53972.49  52638.61  54215.16  52567.02  53377.98  53023.01  53074.73
17536 44140.67 44198.77 43271.99 42354.99 44108.77 43168.55 42292.19 43704.93 43685.43  43721.15  42355.11  42971.60  43090.18  43817.84  42625.80
17537 55598.64 54806.19 55851.53 54241.37 55332.87 55984.72 54634.42 56757.15 55387.88  56542.89  54162.44  55385.74  55104.68  56261.20  56208.95
17538 47201.76 47255.68 46947.10 47393.78 47810.73 45133.31 45659.03 45742.29 43144.94  44795.46  46908.04  46766.95  45996.64  47137.79  45855.75
17539 42966.34 42317.58 42175.05 42218.16 44241.64 42461.95 42275.28 45547.06 41594.54  44401.42  43242.31  44283.07  41873.97  43181.20  44698.16
17540 51720.10 53513.68 53370.62 52499.86 52141.04 52480.77 53459.39 52274.05 51714.26  50763.17  53200.63  53826.32  52726.13  52415.06  52693.39
17541 51886.50 54346.66 52455.07 53257.09 54346.87 53082.60 51224.84 55096.15 50183.70  53459.93  53689.65  55111.22  51968.98  52542.29  53172.53
17542 64674.53 61924.74 62117.34 62218.03 61813.18 60341.01 61346.74 60987.50 60617.65  61526.17  60841.60  61487.52  60390.27  60894.94  61815.17
17543 72859.28 72094.43 71319.20 69323.91 74749.83 70496.33 70783.05 73437.99 69878.12  71951.24  71755.26  72337.07  72122.03  72914.04  72032.61
17544 64530.44 62967.27 60569.80 62546.06 63850.85 63269.77 61765.44 65749.51 62836.42  65296.20  64362.89  62540.15  64885.51  62673.33  64625.73
17545 60997.54 59885.88 62814.28 57506.99 60877.58 62267.27 61800.75 61577.86 60426.46  61398.09  62032.52  61143.87  61002.06  61692.26  61488.73
17546 66210.07 65278.97 65983.38 64292.74 62537.58 64321.77 66217.85 63888.61 68120.92  65442.81  67159.00  67249.44  65290.69  66509.10  64347.03
17547 58391.56 56410.08 57428.55 56040.32 55428.15 54932.81 58843.83 56125.61 57773.13  53353.85  57475.41  56189.07  56258.75  56098.62  56106.02
17548 44503.10 48136.45 44479.90 42780.58 44255.42 46820.19 46342.06 45389.40 46323.09  46694.26  45562.43  46123.28  43995.36  46369.19  45234.70
17549 41052.82 41470.48 42114.75 39178.62 40260.97 42171.58 40928.91 39813.99 40737.32  43167.54  41485.73  42680.95  39005.27  42644.19  42055.35
17550 37759.99 39569.52 40037.50 36666.06 38901.35 38337.06 39729.96 36564.25 38952.40  38447.79  38513.21  40505.52  35735.01  40426.98  37805.07
17551 53585.19 57838.99 55199.40 54424.45 55140.63 56122.79 56466.84 54710.10 59014.78  56657.28  58101.82  57124.09  53953.60  54822.48  54565.31
17552 55068.88 56101.20 55997.94 52059.37 51450.76 56992.29 56167.96 52519.19 57164.56  56634.03  55567.50  56252.24  51849.55  55349.40  54050.45
17553 63357.12 68174.81 65158.11 67029.75 65962.50 63359.01 67217.89 64239.52 67749.00  66885.43  63961.45  66663.14  63612.73  67404.95  65405.66
17554 50059.53 53394.25 55031.61 53433.49 51543.26 52746.32 52311.45 53300.96 55694.59  54160.72  54831.59  55506.13  51418.87  56332.43  51233.70
17555 50985.74 51691.58 54585.70 48157.09 47546.77 50434.94 53857.90 47489.57 55596.19  50930.71  50771.57  51979.88  48241.49  52899.24  47335.25
17556 47252.65 49497.88 48425.57 46495.66 45027.91 48267.12 48719.24 43664.96 50747.32  47853.64  48679.39  48206.76  46268.19  49394.54  47728.10
17557 34989.40 36922.52 37054.20 34143.60 32005.90 35803.63 34787.15 32222.14 37125.44  36779.84  35674.85  36909.22  33210.77  36768.88  33101.08
17558 32311.38 34867.25 34046.65 32237.16 33615.70 32671.68 33842.04 31278.92 36254.90  33395.54  32896.55  34093.92  31450.65  34080.35  32183.45
17559 28985.75 29215.66 29027.48 27177.80 28383.27 28145.54 28245.87 28123.50 28419.19  29418.27  30229.41  29661.48  26845.66  28750.94  30204.18
17560 39258.68 39699.88 38008.05 40013.26 38953.84 36304.98 37512.52 35184.97 36549.57  37433.14  37107.77  37946.42  36536.31  37450.46  38768.06
17561 46164.05 47135.65 45977.53 48632.53 50605.37 45910.67 44192.31 48926.44 45091.88  48157.97  48172.01  48484.05  46676.29  48371.64  46687.04
      Series 16 Series 17 Series 18 Series 19 Series 20 Series 21 Series 22 Series 23 Series 24 Series 25 Series 26 Series 27 Series 28 Series 29
17532  48058.44  47063.84  47838.86  48945.21  46306.68  46077.77  47623.08  46488.93  48009.49  47095.71  48919.34  46476.64  47485.74  47651.84
17533  55175.24  54519.22  54804.92  54863.35  55475.35  55053.70  55864.48  53091.52  56676.10  55801.68  54109.06  55419.69  54718.56  53907.77
17534  46281.19  45675.92  45338.82  45394.25  44505.33  45961.27  45793.16  45130.75  44897.57  46378.32  45595.80  47089.18  44309.91  45131.08
17535  53843.96  53436.78  53507.76  50876.86  54355.19  52886.86  54056.95  53695.03  53213.96  53522.87  51280.17  51913.40  54147.70  53378.58
17536  42799.31  42351.68  43605.10  42062.67  43145.18  43481.83  43394.61  44385.96  43344.67  41569.86  43411.81  43545.04  45146.68  43771.38
17537  56919.38  56122.84  55527.30  55480.87  57432.03  56883.81  56201.70  55861.83  57500.11  54795.13  54451.38  57068.96  55855.83  54796.35
17538  47173.37  45464.13  47914.27  45403.90  46159.19  45966.82  46414.30  43835.29  48494.01  46532.95  44521.65  44264.41  45257.55  47197.84
17539  45205.95  43034.37  43082.33  41622.30  44132.73  43310.28  43901.50  41523.45  45696.54  42201.44  42524.75  42018.02  42609.58  43874.27
17540  52747.87  52156.39  50474.27  51210.11  52210.70  55264.89  51251.45  52752.11  50915.52  52301.34  51139.73  53129.66  52959.49  50953.34
17541  53127.83  50154.45  53096.74  51228.90  53458.96  52970.08  52017.50  50420.38  53468.41  52426.98  52814.72  52085.64  54121.43  51007.62
17542  62021.37  61677.34  61086.24  58979.12  62943.58  63564.18  60729.38  60746.05  61023.39  61229.36  61344.09  63079.62  64170.74  62585.59
17543  75303.91  71220.43  74915.11  68645.91  72957.28  71431.54  72682.64  70697.43  76887.18  71205.57  70908.34  71401.38  70505.30  73871.46
17544  65256.84  61802.24  64590.45  60969.28  63073.04  65405.62  65477.47  63528.67  64581.35  64120.52  62171.03  64972.49  63002.00  64069.23
17545  62031.27  62128.15  62000.25  59388.18  63599.12  60579.57  63844.71  60427.53  60052.87  61600.47  62201.49  59774.64  60060.41  61551.95
17546  65729.58  64535.61  64232.84  64666.72  65718.08  67273.60  65550.08  65609.23  65380.23  64546.23  64511.63  67291.77  66585.62  65695.51
17547  56394.75  57712.74  56673.73  57143.42  56876.28  57106.64  57245.16  58173.00  54265.63  55648.37  58069.12  54669.84  57088.37  57481.16
17548  47764.40  45322.50  44790.42  45297.21  47474.06  46271.51  44309.12  44920.10  46163.96  43790.31  46929.77  44884.55  46839.71  46429.04
17549  40495.93  39967.61  40598.11  40362.51  43740.32  45113.08  40077.55  41288.64  40274.00  42014.69  43306.26  41849.20  42351.86  40592.59
17550  38275.26  38392.26  38159.86  40448.34  37645.53  40677.16  36198.44  37467.38  36449.49  39518.13  41671.50  36521.07  39078.73  39970.11
17551  55479.73  53117.92  54593.79  59746.28  54758.36  55140.15  53876.31  56396.84  53401.93  56212.67  58574.04  54329.39  56711.38  53887.22
17552  53513.79  54035.51  51460.51  59535.49  54206.53  55790.95  52142.01  55279.90  48841.04  56263.29  58246.76  54032.63  55330.65  54072.68
17553  64382.29  67314.27  62151.42  68532.56  67228.75  67527.91  62705.27  67399.20  60768.55  68091.47  69769.69  67695.94  66855.17  63696.61
17554  51939.04  54684.99  53440.36  57502.04  52889.87  50842.49  52196.59  56080.09  47976.09  56648.43  57280.85  51868.53  52165.06  53188.46
17555  49126.11  52368.77  48237.09  52534.27  49245.92  51128.04  49891.01  54087.05  47154.26  49390.66  55262.95  50908.50  50798.64  51373.51
17556  47475.18  48175.90  46150.77  51786.37  49384.77  48305.15  46885.41  50452.45  43039.68  50423.69  51280.02  48588.43  49272.91  46179.53
17557  34551.30  36698.53  34590.41  41451.76  36035.64  35745.39  34113.33  34821.95  33235.14  36635.18  37619.20  36686.93  36313.17  35031.00
17558  32779.71  33812.20  31905.93  36101.86  33723.83  32451.18  31407.53  35202.45  33320.10  31546.89  34649.20  31788.51  33031.72  33534.67
17559  28084.00  27789.18  29000.20  31298.21  29630.42  28965.24  26902.56  27738.50  27791.33  30201.55  29995.33  28716.72  28963.28  29101.04
17560  36992.88  35944.28  37083.80  40025.04  38493.03  39015.76  33782.66  39277.18  39198.44  38206.55  36490.65  40337.09  40110.95  36860.21
17561  45948.33  46822.22  49529.68  46399.51  46067.71  44998.77  45646.66  46538.58  49695.23  47931.84  46186.90  45199.44  46517.80  47065.75
      Series 30
17532  48105.50
17533  55808.81
17534  43460.64
17535  52185.13
17536  43327.63
17537  55874.12
17538  45367.97
17539  42640.42
17540  51502.42
17541  51398.66
17542  60647.43
17543  72686.63
17544  63975.99
17545  60764.58
17546  64103.29
17547  55948.83
17548  45363.19
17549  41059.93
17550  38587.08
17551  57275.83
17552  53306.08
17553  65597.42
17554  52488.70
17555  50372.95
17556  48062.36
17557  34909.85
17558  33487.32
17559  27083.39
17560  36210.35
17561  45251.57

# Create a plot
autoplot(time_series) +
  autolayer(sim)

For a multivariate time series, specify a seriesname for each time series. Defaulting to column names.

# Calculate the average and confidence intervals
sim_mean <- rowMeans(sim)
sim_upper <- apply(sim, 1, quantile, probs = 0.975)
sim_lower <- apply(sim, 1, quantile, probs = 0.025)

# Create a data frame for ggplot2
plot_data <- data.frame(Date = date_index, Mean = sim_mean, Upper = sim_upper, Lower = sim_lower)

# Create a plot
ggplot(plot_data, aes(x = Date, y = Mean)) +
  geom_ribbon(aes(ymin = Lower, ymax = Upper), fill = "blue", alpha = 0.5) +
  geom_line() +
  labs(title = "Time Series with Confidence Intervals", y = "Value") +
  theme_minimal()

plot_data

# Create a plot
ggplot() +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower, ymax = Upper), fill = "blue", alpha = 0.5) +
  geom_line(data = total_sales, aes(x = Date, y = TOTAL), color = "red") +
  labs(title = "Total Sales with Confidence Intervals", y = "Total Sales") +
  theme_minimal()

library(ggplot2)
library(tsibble)
library(dplyr)

# Assuming you have a tsibble named 'total_sales' and a data frame 'plot_data'

# Create a plot with improved aesthetics
ggplot() +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower, ymax = Upper), fill = "blue", alpha = 0.5, color = "blue") +
  geom_line(data = total_sales, aes(x = Date, y = TOTAL), color = "black") +
  labs(title = "Total Sales with Confidence Intervals", y = "Total Sales", fill = "Confidence Intervals") +
  theme_minimal() +
  theme(
    plot.title = element_text(size = 16, hjust = 0.5),
    axis.title.x = element_blank(),
    axis.text.x = element_text(angle = 45, hjust = 1),
    axis.text.y = element_text(size = 12),
    legend.title = element_text(size = 12),
    legend.text = element_text(size = 10)
  ) +
  scale_fill_identity()

library(ggplot2)
library(tsibble)
library(dplyr)

# Assuming you have a tsibble named 'total_sales' and a data frame 'plot_data'

# Define custom colors for the confidence intervals
confidence_colors <- c("blue", "lightblue")  # Adjust colors as needed

# Create a plot with improved aesthetics and a legend
ggplot() +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower, ymax = Upper, fill = "Confidence Intervals"), alpha = 0.5, color = "blue") +
  geom_line(data = total_sales, aes(x = Date, y = TOTAL, color = "Total Sales")) +
  labs(title = "Total Sales with Confidence Intervals", y = "Total Sales") +
  theme_minimal() +
  theme(
    plot.title = element_text(size = 16, hjust = 0.5),
    axis.title.x = element_blank(),
    axis.text.x = element_text(angle = 45, hjust = 1),
    axis.text.y = element_text(size = 12),
    legend.title = element_text(size = 12),
    legend.text = element_text(size = 10)
  ) +
  scale_fill_manual(
    name = "Legend",
    values = setNames(confidence_colors, "Confidence Intervals"),
    breaks = "Confidence Intervals",
    labels = "Confidence Intervals"
  ) +
  scale_color_manual(
    name = "Legend",
    values = setNames("black", "Total Sales"),
    breaks = "Total Sales",
    labels = "Total Sales"
  )

Trying again

# Create a time series with a proper date index
start_date <- as.Date("2018-01-01")  # Change this to your actual start date
sim <- ts(matrix(0, nrow=30, ncol=10), start=start_date)

# Generate simulated data for the time series
for(i in seq(10))
  sim[,i] <- simulate(fit_with_intervals, nsim=30)

library(ggplot2)
library(forecast)

# Create a date index for the time series
date_index <- seq(start_date, by = "days", length.out = 30)
#date_index

# Create a date index for the time series
date_index <- seq(start_date, by = "days", length.out = 30)
# Assign the date index to the time series
time_series <- ts(sim, start = start_date)
#time_series

# Calculate the average and confidence intervals
sim_mean <- rowMeans(sim)
sim_upper <- apply(sim, 1, quantile, probs = 0.975)
sim_lower <- apply(sim, 1, quantile, probs = 0.025)
sim_upper_80 <- apply(sim, 1, quantile, probs = 0.90)
sim_lower_80 <- apply(sim, 1, quantile, probs = 0.10)

# Create a data frame for ggplot2
plot_data <- data.frame(Date = date_index, Mean = sim_mean, Upper_95 = sim_upper, Lower_95 = sim_lower, Upper_80=sim_upper_80, Lower_80=sim_lower_80)

# Create a plot
ggplot(plot_data, aes(x = Date, y = Mean)) +
  geom_ribbon(aes(ymin = Lower_80, ymax = Upper_80), fill = "blue", alpha = 0.5) +
  geom_line() +
  labs(title = "Time Series with Confidence Intervals", y = "Value") +
  theme_minimal()

# Create the plot
ggplot() +
  #geom_line(data = total_sales, aes(x = Date, y = TOTAL), color = "black") +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower_80, ymax = Upper_80), fill = "black", alpha = 0.5) +
  geom_line(data = plot_data, aes(x = Date, y = Mean), color = "black") +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower_95, ymax = Upper_95), fill = "red", alpha = 0.5) +
  labs(
    title = "Total Sales with Confidence Intervals",
    x = "Date",
    y = "Total Sales"
  ) +
  theme_minimal()

# Create the plot
ggplot() +
  #geom_line(data = total_sales, aes(x = Date, y = TOTAL), color = "black") +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower_80, ymax = Upper_80, fill = "80% CI"), alpha = 0.5) +
  geom_line(data = plot_data, aes(x = Date, y = Mean), color = "black") +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower_95, ymax = Upper_95, fill = "95% CI"), alpha = 0.5) +
  labs(
    title = "Total Sales with Confidence Intervals",
    x = "Date",
    y = "Total Sales"
  ) +
  scale_fill_manual(values = c("80% CI" = "blue", "95% CI" = "red")) +
  guides(fill = guide_legend(title = "Confidence Interval")) +
  theme_minimal()

# Create a custom color palette with better contrast
confidence_colors <- c("80% CI" = "#0000ff", "95% CI" = "#0000ff")

# Create the plot
ggplot() +
  geom_line(data = total_sales, aes(x = Date, y = TOTAL), color = "black") +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower_80, ymax = Upper_80, fill = "80% CI"), alpha = 0.5) +
  geom_line(data = plot_data, aes(x = Date, y = Mean), color = "black") +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower_95, ymax = Upper_95, fill = "95% CI"), alpha = 0.5) +
  labs(
    title = "Total Sales with Confidence Intervals",
    x = "Date",
    y = "Total Sales"
  ) +
  scale_fill_manual(values = confidence_colors) +
  guides(fill = guide_legend(title = "Confidence Interval")) +
  theme_minimal()

Interactive

#install.packages("plotly")

# Load the necessary libraries
library(ggplot2)
library(plotly)

# Create a custom color palette with better contrast
confidence_colors <- c("80% CI" = "#3498DB", "95% CI" = "#E74C3C")

# Create the base ggplot object
p <- ggplot() +
  geom_line(data = total_sales, aes(x = Date, y = TOTAL), color = "black") +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower_80, ymax = Upper_80, fill = "80% CI"), alpha = 0.5) +
  geom_line(data = plot_data, aes(x = Date, y = Mean), color = "darkblue") +
  geom_ribbon(data = plot_data, aes(x = Date, ymin = Lower_95, ymax = Upper_95, fill = "95% CI"), alpha = 0.5) +
  labs(
    title = "Future sales forecast with confidence intervals",
    x = "Date",
    y = "Total Sales"
  ) +
  scale_fill_manual(values = confidence_colors) +
  guides(fill = guide_legend(title = "Confidence Interval")) +
  theme_minimal()

# Convert ggplot object to plotly object for interactivity
plotly_plot <- ggplotly(p)

# Display the interactive plot
plotly_plot

NA

FORECASTING confidence intervals

library(forecast)
set.seed(2015)
(forecas_intervals <- nnetar(y=total_sales$TOTAL, lambda=0.5))

Series: total_sales$TOTAL 
Model:  NNAR(20,10) 
Call:   nnetar(y = total_sales$TOTAL, lambda = 0.5)

Average of 20 networks, each of which is
a 20-10-1 network with 221 weights
options were - linear output units 

sigma^2 estimated as 19.91

fcast <- forecast(forecas_intervals, PI=TRUE, h=60)
autoplot(fcast)

autoplot_ts <- autoplot(fcast)
autoplot_ts

THE END