AMZN_Stock_Report
J.Korn
Forecasting a Stock’s Closing Price:
The report below details a exploratory analysis of AMZN stock performance over the past 5 years. The forecast is produced using R to fit three Bayesian structural time series models. The data consists of a .xts times series dataset available through “Yahoo Finance”.
Understand the SP500 Stocks & Extract Stock Symbol…
## 'data.frame': 505 obs. of 9 variables:
## $ Symbol : chr "MMM" "ABT" "ABBV" "ABMD" ...
## $ Security : chr "3M Company" "Abbott Laboratories" "AbbVie Inc." "ABIOMED Inc" ...
## $ SEC.filings : chr "reports" "reports" "reports" "reports" ...
## $ GICS.Sector : chr "Industrials" "Health Care" "Health Care" "Health Care" ...
## $ GICS.Sub.Industry : chr "Industrial Conglomerates" "Health Care Equipment" "Pharmaceuticals" "Health Care Equipment" ...
## $ Headquarters.Location : chr "St. Paul, Minnesota" "North Chicago, Illinois" "North Chicago, Illinois" "Danvers, Massachusetts" ...
## $ Date.first.added.3..4.: chr "" "1964-03-31" "2012-12-31" "2018-05-31" ...
## $ CIK : int 66740 1800 1551152 815094 1467373 718877 796343 2488 1158449 874761 ...
## $ Founded : chr "1902" "1888" "2013 (1888)" "1981" ...## [1] "AMZN"## [1] "Consumer Discretionary"## [1] "Internet & Direct Marketing Retail"Import the Stock Dataset…
## [1] "AMZN"## An 'xts' object on 2014-01-17/2019-01-15 containing:
## Data: num [1:1257, 1:6] 394 403 408 401 398 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:6] "AMZN.Open" "AMZN.High" "AMZN.Low" "AMZN.Close" ...
## Indexed by objects of class: [Date] TZ: UTC
## xts Attributes:
## List of 2
## $ src : chr "yahoo"
## $ updated: POSIXct[1:1], format: "2019-01-16 01:10:58"Exploratory Analysis of Stock Dataset…
Exploratory Analysis of stock dataset - Open Price: 
Exploratory Analysis of stock dataset - Close Price: 
Exploratory Analysis of stock dataset - High Price: 
Exploratory Analysis of stock dataset - Low Price: 
Exploratory Analysis of stock dataset - Volume: 
Exploratory Analysis of stock dataset - Candle Chart - SMA = 20: 
Exploratory Analysis of stock dataset - TA: Added Bollinger Bands, Volume, and Moving Average Convergence Divergence (MACD) plots: 
Exploratory Analysis of stock dataset - Calculate some predictor variables to add to the stock dataset:
## An 'xts' object on 2014-03-31/2019-01-15 containing:
## Data: num [1:1208, 1:18] 342 338 346 342 335 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:18] "Open" "High" "Low" "Close" ...
## Indexed by objects of class: [Date] TZ: UTC
## xts Attributes:
## List of 2
## $ src : chr "yahoo"
## $ updated: POSIXct[1:1], format: "2019-01-16 01:10:58"## Open High Low Close Volume Adjusted daily.returns
## 2014-03-31 342.40 346.29 334.06 336.37 4297500 336.37 -0.005675645
## 2014-04-01 338.09 344.43 338.00 342.99 3600100 342.99 0.019680694
## 2014-04-02 345.99 348.30 340.38 341.96 4475500 341.96 -0.003003000
## 2014-04-03 341.82 342.50 328.46 333.62 6399300 333.62 -0.024388806
## 2014-04-04 335.15 335.44 315.61 323.00 12534600 323.00 -0.031832609
## 2014-04-07 320.99 324.94 313.13 317.76 7077400 317.76 -0.016222879
## atr SMI ADX oscillator pctB
## 2014-03-31 9.991097 -25.76660 25.69594 -50 0.017939734
## 2014-04-01 9.853162 -29.32020 26.94289 -50 0.121687522
## 2014-04-02 9.715078 -32.00644 27.42554 -50 0.188781589
## 2014-04-03 10.024001 -36.05854 28.72464 -75 0.092263203
## 2014-04-04 10.724431 -40.57839 30.60146 -80 0.009346975
## 2014-04-07 10.801971 -45.16075 32.45552 -85 0.006352941
## Delt.1.arithmetic EMA maEMV signal mfi
## 2014-03-31 0.47396283 -0.3505966 -0.10846753 -1.115453 44.20347
## 2014-04-01 0.01500899 -0.1864703 -0.09518293 -1.319675 49.27906
## 2014-04-02 -0.32061697 -0.2618417 -0.07549397 -1.491625 46.64744
## 2014-04-03 0.33102691 -0.2624081 -0.08526839 -1.669376 37.30442
## 2014-04-04 -0.07439208 -0.2610000 -0.07168018 -1.887372 28.46426
## 2014-04-07 -0.30092205 -0.2528033 -0.08081438 -2.140675 23.13613
## sar
## 2014-03-31 368.0574
## 2014-04-01 363.6212
## 2014-04-02 359.8060
## 2014-04-03 356.5250
## 2014-04-04 352.8602
## 2014-04-07 347.4853Exploratory Analysis of stock dataset - Volume: 
Exploratory Analysis of stock dataset - Scatterplot Matrix: 
Train a Bayesian Nowcasting Structural Time Series Model to Forecast Close Price…
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## =-=-=-=-=## $residual.sd
## [1] 8.072437
##
## $prediction.sd
## [1] 21.131
##
## $rsquare
## [1] 0.9997181
##
## $relative.gof
## [1] -0.1648646Plot Model 
## [1] "sigma.obs" "trend.level.sd"
## [3] "trend.slope.mean" "trend.slope.ar.coefficient"
## [5] "trend.slope.sd" "sigma.seasonal.54"
## [7] "final.state" "state.contributions"
## [9] "one.step.prediction.errors" "log.likelihood"
## [11] "has.regression" "state.specification"
## [13] "prior" "timestamp.info"
## [15] "model.options" "family"
## [17] "niter" "original.series"Create Prediction of Close Price Using the Nowcasting Model…
## List of 5
## $ mean : num [1:20] 1648 1663 1670 1668 1665 ...
## $ median : num [1:20] 1647 1660 1670 1659 1667 ...
## $ interval : num [1:2, 1:20] 1624 1671 1625 1700 1628 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:2] "5%" "95%"
## .. ..$ : NULL
## $ distribution : num [1:13, 1:20] 1638 1647 1657 1671 1621 ...
## $ original.series:'zoo' series from 2014-03-31 to 2019-01-15
## Data: num [1:1208] 336 343 342 334 323 ...
## Index: Date[1:1208], format: "2014-03-31" "2014-04-01" ...
## - attr(*, "class")= chr "bsts.prediction"Summary of Prediction:
summary(pred)## Length Class Mode
## mean 20 -none- numeric
## median 20 -none- numeric
## interval 40 -none- numeric
## distribution 260 -none- numeric
## original.series 1208 zoo numericPlot the Mean:
par(mfrow=c(2,2))
plot(pred$original.series)
plot(pred$mean)
plot(pred$median)
plot(pred$interval)
Plot Prediction:
plot(pred, plot.original = 20)
Nowcasting Prediction Table
tail(pred$original.series)## 2019-01-08 2019-01-09 2019-01-10 2019-01-11 2019-01-14 2019-01-15
## 1656.58 1659.42 1656.22 1640.56 1617.21 1674.56head(pred$mean)## [1] 1647.697 1662.810 1670.239 1667.612 1665.439 1679.032head(pred$median)## [1] 1646.865 1660.332 1669.660 1658.682 1667.284 1666.767head(pred$interval)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## 5% 1624.485 1625.388 1628.023 1624.198 1617.774 1622.787 1596.373
## 95% 1670.987 1700.176 1726.799 1718.561 1728.822 1768.324 1774.529
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## 5% 1593.084 1585.814 1576.296 1567.244 1538.910 1553.934 1546.799
## 95% 1768.208 1777.841 1800.035 1774.479 1757.476 1784.294 1805.536
## [,15] [,16] [,17] [,18] [,19] [,20]
## 5% 1552.073 1541.310 1548.405 1551.292 1539.622 1511.209
## 95% 1795.806 1792.998 1807.962 1808.187 1817.056 1826.319Train a Bayesian Regression Structural Time Series Model to Forecast Close Price…
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## =-=-=-=-= Iteration 90 Wed Jan 16 01:12:03 2019
## =-=-=-=-=## $residual.sd
## [1] 4.859581
##
## $prediction.sd
## [1] 16.07452
##
## $rsquare
## [1] 0.9998978
##
## $relative.gof
## [1] 0.3260676
##
## $size
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 1.000 2.000 1.711 2.000 3.000
##
## $coefficients
## mean sd mean.inc sd.inc
## daily.returns 4.110110e+02 66.741371278 411.011024 66.741371
## maEMV 1.287004e+01 11.604097882 18.682321 9.278849
## EMA 3.000435e-02 0.284646210 2.700391 0.000000
## Delt.1.arithmetic -7.668111e-04 0.007274609 -0.069013 0.000000
## sar 0.000000e+00 0.000000000 0.000000 0.000000
## mfi 0.000000e+00 0.000000000 0.000000 0.000000
## signal 0.000000e+00 0.000000000 0.000000 0.000000
## pctB 0.000000e+00 0.000000000 0.000000 0.000000
## oscillator 0.000000e+00 0.000000000 0.000000 0.000000
## ADX 0.000000e+00 0.000000000 0.000000 0.000000
## SMI 0.000000e+00 0.000000000 0.000000 0.000000
## atr 0.000000e+00 0.000000000 0.000000 0.000000
## Adjusted 0.000000e+00 0.000000000 0.000000 0.000000
## Volume 0.000000e+00 0.000000000 0.000000 0.000000
## Low 0.000000e+00 0.000000000 0.000000 0.000000
## High 0.000000e+00 0.000000000 0.000000 0.000000
## Open 0.000000e+00 0.000000000 0.000000 0.000000
## (Intercept) 0.000000e+00 0.000000000 0.000000 0.000000
## inc.prob
## daily.returns 1.00000000
## maEMV 0.68888889
## EMA 0.01111111
## Delt.1.arithmetic 0.01111111
## sar 0.00000000
## mfi 0.00000000
## signal 0.00000000
## pctB 0.00000000
## oscillator 0.00000000
## ADX 0.00000000
## SMI 0.00000000
## atr 0.00000000
## Adjusted 0.00000000
## Volume 0.00000000
## Low 0.00000000
## High 0.00000000
## Open 0.00000000
## (Intercept) 0.00000000Parameter Estimates: (Sample mean of the Sampled beta value)
## (Intercept) Open High Low
## 0.00000000 0.00000000 0.00000000 0.00000000
## Volume Adjusted daily.returns atr
## 0.00000000 0.00000000 375.95080202 0.00000000
## SMI ADX oscillator pctB
## 0.00000000 0.00000000 0.00000000 0.00000000
## Delt.1.arithmetic EMA maEMV signal
## -0.00069013 0.02700391 11.58303895 0.00000000
## mfi sar
## 0.00000000 0.00000000Plot Model 
## [1] "coefficients" "sigma.obs"
## [3] "trend.level.sd" "trend.slope.mean"
## [5] "trend.slope.ar.coefficient" "trend.slope.sd"
## [7] "sigma.seasonal.54" "final.state"
## [9] "state.contributions" "one.step.prediction.errors"
## [11] "log.likelihood" "has.regression"
## [13] "state.specification" "prior"
## [15] "timestamp.info" "model.options"
## [17] "family" "niter"
## [19] "original.series" "xlevels"
## [21] "terms" "predictors"Create Prediction of Close Price Using the Regression Model…
## List of 5
## $ mean : num [1:91] 1645 1634 1636 1630 1645 ...
## $ median : num [1:91] 1645 1635 1635 1624 1644 ...
## $ interval : num [1:2, 1:91] 1638 1652 1620 1650 1618 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:2] "5%" "95%"
## .. ..$ : NULL
## $ distribution : num [1:10, 1:91] 1642 1644 1648 1647 1655 ...
## $ original.series:'zoo' series from 2014-03-31 to 2019-01-15
## Data: num [1:1208] 336 343 342 334 323 ...
## Index: Date[1:1208], format: "2014-03-31" "2014-04-01" ...
## - attr(*, "class")= chr "bsts.prediction"Summary of Prediction:
summary(pred)## Length Class Mode
## mean 91 -none- numeric
## median 91 -none- numeric
## interval 182 -none- numeric
## distribution 910 -none- numeric
## original.series 1208 zoo numericPlot the Mean:
par(mfrow=c(2,2))
plot(pred$original.series)
plot(pred$mean)
plot(pred$median)
plot(pred$interval)
Plot Prediction:
plot(pred, plot.original = 90)
Regression Model Prediction Table
tail(pred$original.series)## 2019-01-08 2019-01-09 2019-01-10 2019-01-11 2019-01-14 2019-01-15
## 1656.58 1659.42 1656.22 1640.56 1617.21 1674.56head(pred$mean)## [1] 1644.993 1633.601 1635.716 1629.532 1645.337 1633.396head(pred$median)## [1] 1645.144 1634.623 1635.216 1624.183 1643.779 1630.252head(pred$interval)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## 5% 1637.666 1619.812 1617.714 1602.361 1619.216 1607.278 1604.497
## 95% 1651.701 1649.560 1653.202 1660.035 1669.694 1663.018 1660.215
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## 5% 1592.501 1557.226 1585.349 1572.160 1573.034 1575.069 1564.167
## 95% 1651.942 1614.964 1655.075 1663.318 1682.174 1697.336 1694.608
## [,15] [,16] [,17] [,18] [,19] [,20] [,21]
## 5% 1567.208 1568.145 1578.433 1587.413 1567.592 1549.350 1539.774
## 95% 1697.583 1697.277 1712.280 1726.864 1725.073 1701.118 1711.866
## [,22] [,23] [,24] [,25] [,26] [,27] [,28]
## 5% 1515.579 1534.879 1488.739 1482.518 1443.019 1467.978 1508.098
## 95% 1693.048 1727.653 1711.212 1696.978 1653.274 1648.666 1710.382
## [,29] [,30] [,31] [,32] [,33] [,34] [,35]
## 5% 1502.854 1549.709 1528.988 1509.788 1518.940 1530.108 1510.649
## 95% 1691.385 1743.226 1754.001 1731.307 1767.963 1783.791 1785.044
## [,36] [,37] [,38] [,39] [,40] [,41] [,42]
## 5% 1481.923 1535.542 1435.515 1405.304 1400.904 1460.016 1489.071
## 95% 1767.630 1828.999 1759.543 1734.627 1733.071 1796.352 1800.781
## [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
## 5% 1484.964 1466.889 1505.262 1549.52 1545.651 1537.414 1534.393 1527.944
## 95% 1791.917 1766.092 1801.530 1832.18 1839.620 1844.724 1819.629 1828.201
## [,51] [,52] [,53] [,54] [,55] [,56] [,57]
## 5% 1487.326 1491.987 1490.320 1434.133 1410.702 1429.593 1413.386
## 95% 1805.244 1794.928 1796.785 1761.274 1738.023 1737.908 1740.420
## [,58] [,59] [,60] [,61] [,62] [,63] [,64]
## 5% 1467.794 1465.123 1520.491 1516.841 1537.715 1592.528 1556.534
## 95% 1790.663 1782.519 1834.164 1841.507 1835.511 1887.061 1855.228
## [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72]
## 5% 1582.505 1553.053 1570.30 1576.177 1561.508 1535.488 1515.568 1474.174
## 95% 1861.556 1825.944 1834.39 1819.084 1816.687 1793.863 1770.756 1725.724
## [,73] [,74] [,75] [,76] [,77] [,78] [,79]
## 5% 1514.049 1516.325 1499.315 1484.929 1467.112 1539.052 1502.015
## 95% 1782.016 1787.797 1786.575 1749.764 1750.446 1820.961 1777.412
## [,80] [,81] [,82] [,83] [,84] [,85] [,86]
## 5% 1544.726 1561.902 1563.079 1551.251 1607.456 1637.555 1672.277
## 95% 1819.366 1826.710 1838.113 1826.148 1882.844 1887.129 1912.900
## [,87] [,88] [,89] [,90] [,91]
## 5% 1659.478 1646.68 1626.508 1604.613 1613.447
## 95% 1898.256 1910.21 1896.201 1876.720 1897.059Train a Modified Bayesian Regression Structural Time Series Model to Forecast Close Price…
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## =-=-=-=-= Iteration 90 Wed Jan 16 01:12:17 2019
## =-=-=-=-=## $residual.sd
## [1] 4.588233
##
## $prediction.sd
## [1] 17.12498
##
## $rsquare
## [1] 0.9999089
##
## $relative.gof
## [1] 0.2352618
##
## $size
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 1.000 1.000 1.011 1.000 2.000
##
## $coefficients
## mean sd mean.inc sd.inc inc.prob
## daily.returns 4.117891e+02 6.903792e+01 4.117891e+02 69.03792 1.00000000
## Adjusted 5.631126e-06 5.342155e-05 5.068013e-04 0.00000 0.01111111
## Volume 0.000000e+00 0.000000e+00 0.000000e+00 0.00000 0.00000000
## (Intercept) 0.000000e+00 0.000000e+00 0.000000e+00 0.00000 0.00000000Parameter Estimates: (Sample mean of the Sampled beta value)
## (Intercept) Volume Adjusted daily.returns
## 0.000000e+00 0.000000e+00 5.068013e-06 3.743886e+02Plot Model 
## [1] "coefficients" "sigma.obs"
## [3] "trend.level.sd" "trend.slope.mean"
## [5] "trend.slope.ar.coefficient" "trend.slope.sd"
## [7] "sigma.seasonal.54" "final.state"
## [9] "state.contributions" "one.step.prediction.errors"
## [11] "log.likelihood" "has.regression"
## [13] "state.specification" "prior"
## [15] "timestamp.info" "model.options"
## [17] "family" "niter"
## [19] "original.series" "xlevels"
## [21] "terms" "predictors"Create Prediction of Close Price Using the Modified Regression Model…
## List of 5
## $ mean : num [1:91] 1640 1658 1659 1663 1669 ...
## $ median : num [1:91] 1638 1655 1667 1664 1686 ...
## $ interval : num [1:2, 1:91] 1635 1646 1654 1664 1641 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:2] "5%" "95%"
## .. ..$ : NULL
## $ distribution : num [1:3, 1:91] 1638 1646 1634 1654 1665 ...
## $ original.series:'zoo' series from 2014-03-31 to 2019-01-15
## Data: num [1:1208] 336 343 342 334 323 ...
## Index: Date[1:1208], format: "2014-03-31" "2014-04-01" ...
## - attr(*, "class")= chr "bsts.prediction"Summary of Prediction:
summary(pred)## Length Class Mode
## mean 91 -none- numeric
## median 91 -none- numeric
## interval 182 -none- numeric
## distribution 273 -none- numeric
## original.series 1208 zoo numericPlot the Mean:
par(mfrow=c(2,2))
plot(pred$original.series)
plot(pred$mean)
plot(pred$median)
plot(pred$interval)
Plot Prediction:
plot(pred, plot.original = 90)
Regression Model Prediction Table
tail(pred$original.series)## 2019-01-08 2019-01-09 2019-01-10 2019-01-11 2019-01-14 2019-01-15
## 1656.58 1659.42 1656.22 1640.56 1617.21 1674.56head(pred$mean)## [1] 1639.542 1657.653 1659.187 1662.982 1669.032 1674.833head(pred$median)## [1] 1637.898 1654.731 1666.911 1664.462 1686.134 1675.067head(pred$interval)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## 5% 1634.725 1653.742 1640.763 1654.217 1638.460 1664.753 1667.457
## 95% 1645.511 1663.609 1672.205 1670.711 1687.632 1684.749 1704.510
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## 5% 1667.245 1657.949 1707.632 1692.120 1673.744 1674.902 1692.977
## 95% 1701.789 1696.966 1734.604 1726.659 1736.292 1775.381 1808.173
## [,15] [,16] [,17] [,18] [,19] [,20] [,21]
## 5% 1677.929 1666.170 1685.478 1684.917 1668.421 1662.597 1654.785
## 95% 1817.774 1834.271 1849.894 1883.914 1888.898 1887.170 1914.209
## [,22] [,23] [,24] [,25] [,26] [,27] [,28]
## 5% 1655.553 1676.935 1683.379 1669.702 1666.775 1695.829 1722.242
## 95% 1901.781 1920.424 1941.317 1927.478 1929.046 1914.113 1948.973
## [,29] [,30] [,31] [,32] [,33] [,34] [,35]
## 5% 1687.468 1694.596 1669.106 1629.262 1681.596 1697.637 1708.560
## 95% 1942.804 1962.260 1944.463 1919.017 1941.740 1930.685 1918.916
## [,36] [,37] [,38] [,39] [,40] [,41] [,42]
## 5% 1699.686 1757.285 1704.146 1740.910 1777.847 1787.356 1802.062
## 95% 1888.806 1953.135 1888.905 1902.788 1920.964 1947.996 1931.314
## [,43] [,44] [,45] [,46] [,47] [,48] [,49]
## 5% 1797.566 1795.184 1818.850 1833.486 1810.752 1782.963 1765.950
## 95% 1924.562 1908.968 1931.739 1940.983 1922.756 1910.042 1930.601
## [,50] [,51] [,52] [,53] [,54] [,55] [,56]
## 5% 1795.319 1772.498 1770.460 1739.349 1735.981 1741.512 1763.216
## 95% 1963.240 1955.510 1974.841 1954.975 1968.294 1980.331 2012.772
## [,57] [,58] [,59] [,60] [,61] [,62] [,63]
## 5% 1749.258 1774.807 1721.925 1760.752 1743.568 1738.757 1757.204
## 95% 2010.552 2048.304 2035.619 2059.880 2045.209 2083.170 2091.823
## [,64] [,65] [,66] [,67] [,68] [,69] [,70]
## 5% 1718.417 1751.015 1701.140 1733.931 1719.517 1705.912 1714.806
## 95% 2057.067 2069.223 2018.476 2061.502 2029.472 2015.072 2021.676
## [,71] [,72] [,73] [,74] [,75] [,76] [,77]
## 5% 1683.736 1691.949 1727.034 1723.320 1770.750 1746.266 1781.411
## 95% 1996.125 1996.290 2011.280 1992.492 2028.344 2005.983 2046.419
## [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85]
## 5% 1861.217 1798.334 1819.611 1793.84 1795.757 1746.565 1774.856 1765.919
## 95% 2115.763 2048.151 2065.931 2056.97 2073.269 2040.930 2074.952 2054.184
## [,86] [,87] [,88] [,89] [,90] [,91]
## 5% 1737.271 1751.688 1746.380 1742.171 1748.134 1775.221
## 95% 2021.611 2035.737 2033.237 2038.861 2029.676 2080.175