R Time Series Objects vs Data Frames: Advantages and Limitations

Get a Time Series Object

At its most basic, a time series object is a list or sometimes matrix of observations at regular time intervals.

Examples in built-in R data sets include:

• annual Nile river flows

class(Nile)

## [1] "ts"

str(Nile)

##  Time-Series [1:100] from 1871 to 1970: 1120 1160 963 1210 1160 1160 813 1230 1370 1140 ...

Nile

## Time Series:
## Start = 1871 
## End = 1970 
## Frequency = 1 
##   [1] 1120 1160  963 1210 1160 1160  813 1230 1370 1140  995  935 1110  994 1020
##  [16]  960 1180  799  958 1140 1100 1210 1150 1250 1260 1220 1030 1100  774  840
##  [31]  874  694  940  833  701  916  692 1020 1050  969  831  726  456  824  702
##  [46] 1120 1100  832  764  821  768  845  864  862  698  845  744  796 1040  759
##  [61]  781  865  845  944  984  897  822 1010  771  676  649  846  812  742  801
##  [76] 1040  860  874  848  890  744  749  838 1050  918  986  797  923  975  815
##  [91] 1020  906  901 1170  912  746  919  718  714  740

• monthly Air Passengers - yes, I know everybody uses Air Passengers for their time series example. So damn handy. Different examples below, I promise. ;)

class(AirPassengers)

## [1] "ts"

str(AirPassengers)

##  Time-Series [1:144] from 1949 to 1961: 112 118 132 129 121 135 148 148 136 119 ...

AirPassengers

##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1949 112 118 132 129 121 135 148 148 136 119 104 118
## 1950 115 126 141 135 125 149 170 170 158 133 114 140
## 1951 145 150 178 163 172 178 199 199 184 162 146 166
## 1952 171 180 193 181 183 218 230 242 209 191 172 194
## 1953 196 196 236 235 229 243 264 272 237 211 180 201
## 1954 204 188 235 227 234 264 302 293 259 229 203 229
## 1955 242 233 267 269 270 315 364 347 312 274 237 278
## 1956 284 277 317 313 318 374 413 405 355 306 271 306
## 1957 315 301 356 348 355 422 465 467 404 347 305 336
## 1958 340 318 362 348 363 435 491 505 404 359 310 337
## 1959 360 342 406 396 420 472 548 559 463 407 362 405
## 1960 417 391 419 461 472 535 622 606 508 461 390 432

Both these examples are time series of the ts class, and we can see right off that these are different data structures from data frames. A key thing to note about time series is that date/time is not in a column the way it would be in a data frame, but is in an index - similar to row.names in a data frame.

If we look at the index for the Nile river data, we can see the time values and we can check the start and end. This info corresponds to the structure info shown above, where start = 1871, end = 1970, and frequency = 1, meaning 1 observation per year, annual data.

index(Nile)

##   [1] 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885
##  [16] 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900
##  [31] 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915
##  [46] 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930
##  [61] 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945
##  [76] 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960
##  [91] 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970

start(Nile)

## [1] 1871    1

end(Nile)

## [1] 1970    1

As discussed above, ts is useful, but xts offers additional flexibility and features.

Convert ts to xts

Converting to an xts object can often make the data more intuitive to deal with.

library(xts)
Nile_xts <- as.xts(Nile)
str(Nile_xts)

## An 'xts' object on 1871-01-01/1970-01-01 containing:
##   Data: num [1:100, 1] 1120 1160 963 1210 1160 1160 813 1230 1370 1140 ...
##   Indexed by objects of class: [Date] TZ: UTC
##   xts Attributes:  
##  NULL

head(Nile_xts)

##            [,1]
## 1871-01-01 1120
## 1872-01-01 1160
## 1873-01-01  963
## 1874-01-01 1210
## 1875-01-01 1160
## 1876-01-01 1160

Air_xts <- as.xts(AirPassengers)
str(Air_xts)

## An 'xts' object on Jan 1949/Dec 1960 containing:
##   Data: num [1:144, 1] 112 118 132 129 121 135 148 148 136 119 ...
##   Indexed by objects of class: [yearmon] TZ: UTC
##   xts Attributes:  
##  NULL

head(Air_xts)

##          [,1]
## Jan 1949  112
## Feb 1949  118
## Mar 1949  132
## Apr 1949  129
## May 1949  121
## Jun 1949  135

• We can see here that xts has reshaped the data from a matrix with rows by year and columns by month to more ‘tidy’ data with mth-year as index and observations in one column.

Native xts

Some data comes as xts time series out of the box. For example, the quantmod package fetches stock market data as xts time series automatically:

library(quantmod)
## use quantmod pkg to get some stock prices as time series
price <- getSymbols(Symbols='EA', from="2020-01-01", to=Sys.Date(), auto.assign=FALSE)
class(price)

## [1] "xts" "zoo"

head(price)

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-01-02     108     108    107      107   1901000         107
## 2020-01-03     106     108    105      107   1840300         107
## 2020-01-06     107     109    107      109   2934200         108
## 2020-01-07     109     109    108      108   1692400         108
## 2020-01-08     108     110    108      109   2651600         109
## 2020-01-09     110     110    108      109   1818600         109

As noted, a key characteristic of time series object is that dates are in an index rather than being in a date column, as they would be in typical data frame. Looking at the structure of the xts object, we can again see it is different from a data frame.

str(price)

## An 'xts' object on 2020-01-02/2022-02-04 containing:
##   Data: num [1:529, 1:6] 108 106 107 109 108 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:6] "EA.Open" "EA.High" "EA.Low" "EA.Close" ...
##   Indexed by objects of class: [Date] TZ: UTC
##   xts Attributes:  
## List of 2
##  $ src    : chr "yahoo"
##  $ updated: POSIXct[1:1], format: "2022-02-05 17:47:53"

Convert xts to data frame

If you want to work with the time series as a data frame, it is fairly straightforward to convert an xts object:

price_df <- as.data.frame(price)
## add Date field based on index (row names) of xts object
price_df$Date <- index(price)
## set data frame row names to numbers instead of dates
rownames(price_df) <- seq(1:nrow(price))
## reorder columns to put Date first
price_df <- price_df %>% select(Date, 1:ncol(price_df)-1)
## check out structure using glimpse, as is the fashion of the times
glimpse(price_df)

## Rows: 529
## Columns: 7
## $ Date        <date> 2020-01-02, 2020-01-03, 2020-01-06, 2020-01-07, 2020-01-0…
## $ EA.Open     <dbl> 108, 106, 107, 109, 108, 110, 109, 109, 110, 110, 110, 112…
## $ EA.High     <dbl> 108, 108, 109, 109, 110, 110, 109, 110, 110, 110, 111, 113…
## $ EA.Low      <dbl> 107, 105, 107, 108, 108, 108, 108, 109, 109, 109, 110, 112…
## $ EA.Close    <dbl> 107, 107, 109, 108, 109, 109, 109, 110, 110, 110, 111, 113…
## $ EA.Volume   <dbl> 1901000, 1840300, 2934200, 1692400, 2651600, 1818600, 1756…
## $ EA.Adjusted <dbl> 107, 107, 108, 108, 109, 109, 108, 109, 109, 109, 111, 112…

Data frame is basically a straight-up table, whereas the xts object has other structural features.

Convert data frame to xts

## convert data frame to xts object by specifying the date field to use for xts index.
price_xts <- xts(price_df, order.by=as.Date(price_df$Date))
str(price_xts)

## An 'xts' object on 2020-01-02/2022-02-04 containing:
##   Data: chr [1:529, 1:7] "2020-01-02" "2020-01-03" "2020-01-06" "2020-01-07" ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:7] "Date" "EA.Open" "EA.High" "EA.Low" ...
##   Indexed by objects of class: [Date] TZ: UTC
##   xts Attributes:  
##  NULL

Notice, however, that in the process of converting an xts object to data frame and back to xts, the xts Attributes information has been lost.

Saving/Exporting time series data

Due to the structure of an xts object, the best way to save/export for future use in R and preserve all its attributes is to save as RDS file, using saveRDS. (additional helpful RDS info here.)

However, this won’t be helpful if you need to share the data with someone who is not using R. You can save as a CSV file using write.zoo (be sure to specificy sep=“,”) and this will maintain the table structure of the data but will drop the attributes. It will automatically move the indexes into an Index column so if someone opens it in Excel/Google Sheets, they will see the dates/times.

Saving as RDS or CSV:

## save as RDS to preserve attributes
saveRDS(price, file="price.rds")
price_rds <- readRDS(file='price.rds')
str(price_rds)

## An 'xts' object on 2020-01-02/2022-02-04 containing:
##   Data: num [1:529, 1:6] 108 106 107 109 108 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:6] "EA.Open" "EA.High" "EA.Low" "EA.Close" ...
##   Indexed by objects of class: [Date] TZ: UTC
##   xts Attributes:  
## List of 2
##  $ src    : chr "yahoo"
##  $ updated: POSIXct[1:1], format: "2022-02-05 17:47:53"

## save as CSV - ensure to include sep=","
write.zoo(price, file='price.csv', sep=",")
price_zoo <- read_csv('price.csv')

Period/Frequency Manipulation

Change the period granularity to less granular:

• easily change daily data to weekly, monthly, quarterly, yearly

## get periodicity (frequency) for data set
periodicity(price)

## Daily periodicity from 2020-01-02 to 2022-02-04

## aggregate by period
head(to.weekly(price)[,1:5])

##            price.Open price.High price.Low price.Close price.Volume
## 2020-01-03        108        108       105         107      3741300
## 2020-01-10        107        110       107         109     10852800
## 2020-01-17        109        113       109         113     10221500
## 2020-01-24        113        114       112         112      8457000
## 2020-01-31        110        113       106         108     18435600
## 2020-02-07        108        111       104         109     15973600

head(to.monthly(price)[,1:5])

##          price.Open price.High price.Low price.Close price.Volume
## Jan 2020      107.9        114     105.1         108     51708200
## Feb 2020      107.9        111      98.6         101     55140000
## Mar 2020      101.9        112      85.7         100    116497800
## Apr 2020       98.4        119      96.7         114     72981400
## May 2020      113.1        123     111.1         123     71400200
## Jun 2020      123.3        134     113.3         132     64143400

head(to.yearly(price)[,1:5])

##            price.Open price.High price.Low price.Close price.Volume
## 2020-12-31        108        147      85.7         144    747474600
## 2021-12-31        143        150     120.1         132    641690300
## 2022-02-04        132        143     125.6         138     72451300

Notice that this isn’t a straight roll-up but actual summary: for the monthly data, the High is max of daily data for the month, the Low is minimum for the month, while volume is the sum for the month, all as you would expect.

You can also pull out the values at the END of a period-length, including setting number of periods to skip over each iteration:

• get index for last day of period length specified in ‘on’ for every k period.
• apply index to dataset to extract the rows.

## every 2 weeks (on='week's, k=2)
end_wk <- endpoints(price, on="weeks", k=2)
head(price[end_wk,])

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-01-03   105.6   107.8  105.1    107.2   1840300       106.5
## 2020-01-17   112.4   113.0  111.6    112.9   3053300       112.2
## 2020-01-31   110.8   110.8  105.5    107.9   6995800       107.2
## 2020-02-14   108.9   109.9  108.8    109.7   1227500       109.0
## 2020-02-28   100.3   101.9   98.6    101.4   6853700       100.7
## 2020-03-13    98.7    99.6   92.8     97.1   5842000        96.5

## every 6 months
end_mth <- endpoints(price, on='months', k=6)
head(price[end_mth,])

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-06-30     133     133    131      132   2177400         131
## 2020-12-31     142     144    142      144   1689900         143
## 2021-06-30     144     145    143      144   1799900         143
## 2021-12-31     134     135    132      132   1610900         132

See end of Period Calculations section for how to get an average during periods shown: averages for each 6 month period, for example.

Period Counts

## get the number of weeks, months, years in the dataset (including partial)
price_nw <- nweeks(price)
price_nm <- nmonths(price)
price_ny <- nyears(price)

The price data covers:

• 529 days
• 110 weeks
• 26 months
• 3 years (or portions thereof)

First/last dates:

## get earliest date
st_date <- start(price)
## get last date
end_date <- end(price)

• Start: 2020-01-02
• End: 2022-02-04

Selecting/Subsetting

Time series objects make it easy to slice the data by date ranges. This is an area where time series really shine compared to trying to do the same thing with a data frame.

• xts is super-efficient at interpreting date ranges based on minimal info.
• ‘/’ is a key symbol for separating dates - it is your friend.
• date ranges are inclusive of references used.

Note that in the following examples based on stock market data, dates are missing due to gaps in data - days when markets closed.

• quickly get entire YEAR

## subset on a YEAR (showing head and tail to confirm data is 2021 only)
head(price["2021"])

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2021-01-04     143     144    138      140   3587000         139
## 2021-01-05     140     141    138      141   2117800         141
## 2021-01-06     139     140    136      137   2398500         136
## 2021-01-07     137     141    137      141   2936200         140
## 2021-01-08     141     142    140      142   1902700         141
## 2021-01-11     142     142    139      141   2589800         141

tail(price["2021"])

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2021-12-23     131     133    131      133   1594000         133
## 2021-12-27     133     134    132      133   1377300         133
## 2021-12-28     133     135    133      133   1230700         133
## 2021-12-29     134     134    132      133    912300         133
## 2021-12-30     134     136    134      134   1177000         134
## 2021-12-31     134     135    132      132   1610900         132

• DURING selected month

## get data DURING selected month
price["2020-02"]

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-02-03     108     109  104.4      105   4155500         104
## 2020-02-04     106     107  105.3      107   4190500         106
## 2020-02-05     109     109  107.1      108   2895700         107
## 2020-02-06     109     110  108.4      110   2500600         109
## 2020-02-07     109     111  108.7      109   2231300         108
## 2020-02-10     109     110  108.2      109   2170800         108
## 2020-02-11     109     109  107.9      109   1195300         108
## 2020-02-12     110     110  108.6      110   1567200         109
## 2020-02-13     109     109  108.0      109   1627000         108
## 2020-02-14     109     110  108.8      110   1227500         109
## 2020-02-18     109     110  108.7      109   2171400         109
## 2020-02-19     110     111  109.4      110   1540000         109
## 2020-02-20     109     109  107.4      109   4034000         109
## 2020-02-21     108     109  106.8      108   2546900         107
## 2020-02-24     105     108  105.0      107   2817100         106
## 2020-02-25     108     109  105.2      105   3651300         105
## 2020-02-26     106     108  105.6      107   2858000         106
## 2020-02-27     104     106  102.7      103   4906200         102
## 2020-02-28     100     102   98.6      101   6853700         101

• FROM start of year to END OF SPECIFIC MONTH

## get data FROM start of a year to END OF SPECIFIC MONTH
price_jf <- price["2021/2021-02"]
head(price_jf, 4)

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2021-01-04     143     144    138      140   3587000         139
## 2021-01-05     140     141    138      141   2117800         141
## 2021-01-06     139     140    136      137   2398500         136
## 2021-01-07     137     141    137      141   2936200         140

tail(price_jf, 3)

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2021-02-24     138     140    137      138   3735500         137
## 2021-02-25     137     139    134      135   3042600         135
## 2021-02-26     136     138    134      134   3646600         133

• everything BEFORE specified date

## get everything BEFORE specified date (based on what is avaliable)
price["/2020-01-06"]

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-01-02     108     108    107      107   1901000         107
## 2020-01-03     106     108    105      107   1840300         107
## 2020-01-06     107     109    107      109   2934200         108

• everything BETWEEN two dates

## get everything BETWEEN two dates
price["2021-06-01/2021-06-04"]

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2021-06-01     142     144    142      144   2610300         143
## 2021-06-02     144     144    141      141   1522100         141
## 2021-06-03     141     143    141      142   1574900         142
## 2021-06-04     143     146    143      145   1919500         145

• everything AFTER specified date

## get everything AFTER specified date
price["2022-01-18/"]

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2022-01-18     138     143    133      134   8758900         134
## 2022-01-19     136     138    135      137   3820300         137
## 2022-01-20     138     142    138      139   3116900         139
## 2022-01-21     138     141    138      139   3120000         139
## 2022-01-24     137     139    132      135   4262100         135
## 2022-01-25     134     134    130      131   2386400         131
## 2022-01-26     131     132    129      130   2333800         130
## 2022-01-27     131     134    131      131   1781500         131
## 2022-01-28     131     132    130      132   2155000         132
## 2022-01-31     131     136    129      133   4471000         133
## 2022-02-01     133     133    129      130   3828000         130
## 2022-02-02     126     138    126      137   5723700         137
## 2022-02-03     135     140    134      137   3409200         137
## 2022-02-04     135     138    135      138   2396700         138

Period Calculations

Time series objects lend themselves well to time-based calculations.

Simple arithmetic between two dates is not as straightforward as might be expected, but still easily doable:

## subtraction of a given metric between two dates
as.numeric(price$EA.Close["2022-01-21"])-as.numeric(price$EA.Close["2022-01-18"])

## [1] 5.1

## subtraction of one metric from another on same date
price$EA.Close["2022-01-18"]-price$EA.Open["2022-01-18"]

##            EA.Close
## 2022-01-18    -4.53

Lag.xts is versatile for lag calculations, calculating differences over time:

## calculates across all columns with one command - default is 1 period but can be set with k
head(price-lag.xts(price))

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-01-02      NA      NA     NA       NA        NA          NA
## 2020-01-03   -2.36   -0.60  -1.64    -0.14    -60700      -0.139
## 2020-01-06    1.37    1.56   1.51     1.58   1093900       1.570
## 2020-01-07    2.05   -0.06   1.10    -0.39  -1241800      -0.388
## 2020-01-08   -0.82    0.75   0.05     1.10    959200       1.093
## 2020-01-09    1.82    0.34   0.49    -0.13   -833000      -0.129

## set k for longer lag - this example starting at a date beyond available data for the lag calculations, so no NAs
head(price["2020-01-13/"]-lag.xts(price, k=7))

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-01-13    1.11    1.72   1.86     2.48    -43600       2.464
## 2020-01-14    4.08    2.42   3.59     2.38   -116900       2.365
## 2020-01-15    2.84    1.14   2.51     0.83  -1455100       0.825
## 2020-01-16    1.00    2.04   2.22     2.87    415900       2.852
## 2020-01-17    4.19    2.99   3.77     3.44    401700       3.418
## 2020-01-21    2.55    2.63   3.50     3.05    346400       3.031

## works for individual column
price$EA.Close["2022-01-18/"]-lag.xts(price$EA.Close, k=2)

##            EA.Close
## 2022-01-18     3.07
## 2022-01-19     6.47
## 2022-01-20     4.97
## 2022-01-21     2.10
## 2022-01-24    -3.68
## 2022-01-25    -8.00
## 2022-01-26    -5.22
## 2022-01-27     0.05
## 2022-01-28     1.94
## 2022-01-31     1.60
## 2022-02-01    -1.98
## 2022-02-02     4.51
## 2022-02-03     7.35
## 2022-02-04     0.54

Diff for calculating differences, based on combination of lag and difference order:

head(diff(price, lag=1, differences=1))

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-01-02      NA      NA     NA       NA        NA          NA
## 2020-01-03   -2.36   -0.60  -1.64    -0.14    -60700      -0.139
## 2020-01-06    1.37    1.56   1.51     1.58   1093900       1.570
## 2020-01-07    2.05   -0.06   1.10    -0.39  -1241800      -0.388
## 2020-01-08   -0.82    0.75   0.05     1.10    959200       1.093
## 2020-01-09    1.82    0.34   0.49    -0.13   -833000      -0.129

head(diff(price, lag=1, differences=2))

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-01-02      NA      NA     NA       NA        NA          NA
## 2020-01-03      NA      NA     NA       NA        NA          NA
## 2020-01-06    3.73    2.16   3.15     1.72   1154600        1.71
## 2020-01-07    0.68   -1.62  -0.41    -1.97  -2335700       -1.96
## 2020-01-08   -2.87    0.81  -1.05     1.49   2201000        1.48
## 2020-01-09    2.64   -0.41   0.44    -1.23  -1792200       -1.22

• first example: diff with lag=1, differences=1 gives same result as lag.xts with k=1 (or default)
• second example: diff with differences=2 gives the ‘second order difference’: difference between the differences.
  • EA.Open:
    • 3.73 = 1.37-(-2.36)
    • 0.68 = 2.05-1.37
    • -2.87 = -0.82-2.05
    • …

Useful for some forecasting methods, among other applications.

Returns for calculating % change period over period:

• functions in quantmod package designed for financial asset prices, but can be applied to other xts data.
• various periodicity: daily, weekly, monthly, quarterly, yearly or ALL at once (allReturn())

head(dailyReturn(price))

##            daily.returns
## 2020-01-02      -0.00556
## 2020-01-03      -0.00130
## 2020-01-06       0.01474
## 2020-01-07      -0.00359
## 2020-01-08       0.01015
## 2020-01-09      -0.00119

head(monthlyReturn(price))

##            monthly.returns
## 2020-01-31       -0.000185
## 2020-02-28       -0.060693
## 2020-03-31       -0.011838
## 2020-04-30        0.140661
## 2020-05-29        0.075442
## 2020-06-30        0.074626

• applied to Air Passenger xts to get % change, even though not financial returns:

head(monthlyReturn(Air_xts))

##          monthly.returns
## Jan 1949          0.0000
## Feb 1949          0.0536
## Mar 1949          0.1186
## Apr 1949         -0.0227
## May 1949         -0.0620
## Jun 1949          0.1157

Average for period:

• Using the indexes obtained in the ‘endpoints’ example at the end of the Period/Frequency Manipulation section above, calculate averages for the periods.

period.apply(price, INDEX=end_mth, FUN=mean)

##            EA.Open EA.High EA.Low EA.Close EA.Volume EA.Adjusted
## 2020-06-30     111     113    110      112   3454968         111
## 2020-12-31     133     134    131      133   2465653         132
## 2021-06-30     140     142    139      140   2508342         140
## 2021-12-31     138     139    136      137   2583249         137
## 2022-02-04     133     136    131      133   3018804         133

Rolling Average:

You can also calculate a rolling (moving) average quickly with ‘rollmean’ function from zoo:

## get subset of data for demo
price_c <- price[,'EA.Close']
price_c <- price_c['/2020-02-28']
## calc rolling mean and add to original data 
## - k=3 means 3-period lag
## - align='right' put calculated number at last date in rolling period
price_c$EA_CLose_rm <- rollmean(price_c, k=3, align='right')

## quick dygraph - more on this below
dygraph(price_c, width='100%')

Plot.ts

You can do a quick, simple plot with plot.ts(). Note that in this case the x-axis is the numerical index of the data point, and doesn’t show the date.

plot.ts(price$EA.Close)

Dygraphs

The dygraphs package offers flexibility and interactivity for time series.

• easily show multiple metrics at once.
• scroll over to see details.
• select chart area to zoom in.

library(dygraphs)
dygraph(price[,1:4], width='100%')

• subset for individual columns.
• easily add annotations for events.

## use dyEvent to add annotations
graph <- dygraph(price$EA.Close, width='100%')
graph <- dyEvent(graph, "2020-02-21","Start of Covid 19", labelLoc = 'top')
graph <- dyEvent(graph, "2021-06-10","New product announcements", labelLoc = 'top')
## print chart
graph

Get an ARIMA Model

Some basic terms, over-simplified for our purposes here:

• ARIMA stands for Auto Regression Integrated Moving Average
• One of the most widely-used time series forecasting methods, although certainly not the only.
• 3 essential parameters for ARIMA are p,d,q: p=periods of lag, d=differencing, q=error of the model.

library(forecast)
## get closing prices for forecasting
price_cl <- price[,4]
## get a model for the time series - using auto.arima for simplicity
fitA <- auto.arima(price_cl, seasonal=FALSE) ## can add trace=TRUE to see comparison of different models 
## show model
fitA

## Series: price_cl 
## ARIMA(0,1,1) 
## 
## Coefficients:
##          ma1
##       -0.089
## s.e.   0.043
## 
## sigma^2 estimated as 5.69:  log likelihood=-1208
## AIC=2420   AICc=2420   BIC=2428

The model we get back is ARIMA(0,1,1) which means p=0, d=1, q=1. We can generate a model by setting these parameters manually, but auto.arima automatically checks a variety of models and selects the best. When comparing models, lowest AIC and BIC are preferred.

We can check the accuracy of the model. Most useful item here for interpretation and comparison is MAPE (mean average percent error). In this case,

## check accuracy - based on historical data
accuracy(fitA)

##                  ME RMSE  MAE    MPE MAPE  MASE     ACF1
## Training set 0.0631 2.38 1.76 0.0311 1.39 0.999 -0.00216

fitAa <- accuracy(fitA)
100-fitAa[,5]

## [1] 98.6

So in this case a MAPE of 1.39 can be seen as accuracy of 98.61%.

We can also plot the residuals of the model for visual inspection.

## check residuals
tsdisplay(residuals(fitA), main='Residuals of Simple ARIMA Forecasting Model for Stock Price')

As usual with residuals, we are looking for mean around 0, roughly evenly distributed. For ARIMA we also get ACF and PACF, where we are looking for bars to be short and at least within blue dotted lines. So looks like we are good to go here.

Create A Forecast

We just need a little more code to create and plot forecast. We can set the forecast period for whatever we want, based on the periodicity of the data, in this case days and we are looking out 30 days.

days=30
fcastA <- forecast(fitA, h=days)
plot(fcastA)

That was easy! And we can use this approach to quickly iterate over various models, if we are not convinced that auto.arima is the best. Of course you can use data frames to create forecasts of various sorts but the xts object makes it super-easy to apply common time series methods.

This also reveals a shortcoming of times-series forecasting:

• dependence of pattern recognition and pattern repetition, which can lead to conservative forecast, especially with noisy data.
• as a result, the forecast is: ‘steady as she goes, with possibility of moving either quite a bit higher or quite a bit lower’.

So not that useful. To be fair, if stock market prices are not actually predictable, so it is a perfectly reasonable outcome that grounds us in reality.