MiniClass 5
Senet Manandhar
Introduction to Time Series
Data Received: FRED (https://fred.stlouisfed.org/)
What is Time Series?
Time Series is a sequence of data in chronological order where data is recorded over time.
library(readr)
UNEMP<- read_csv("C:/Users/senet/Desktop/CSC 463 Data Visualization Tools/R/Mini Class 5/UNEMP.csv")## Parsed with column specification:
## cols(
## DATE = col_character(),
## UNRATE = col_double()
## )Changing the table UNEMP (Unemployment) into a time series data “ts”
class(UNEMP)## [1] "tbl_df" "tbl" "data.frame"URATE<-ts(UNEMP$UNRATE,start=c(1948,1), end=c(2017,09),freq=12)head(UNEMP)## # A tibble: 6 x 2
## DATE UNRATE
## <chr> <dbl>
## 1 1/1/1948 3.4
## 2 2/1/1948 3.8
## 3 3/1/1948 4.0
## 4 4/1/1948 3.9
## 5 5/1/1948 3.5
## 6 6/1/1948 3.6head(URATE)## [1] 3.4 3.8 4.0 3.9 3.5 3.6Plotting Unemployement rate in time series plot
plot(URATE)
decompose(URATE)## $x
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1948 3.4 3.8 4.0 3.9 3.5 3.6 3.6 3.9 3.8 3.7 3.8 4.0
## 1949 4.3 4.7 5.0 5.3 6.1 6.2 6.7 6.8 6.6 7.9 6.4 6.6
## 1950 6.5 6.4 6.3 5.8 5.5 5.4 5.0 4.5 4.4 4.2 4.2 4.3
## 1951 3.7 3.4 3.4 3.1 3.0 3.2 3.1 3.1 3.3 3.5 3.5 3.1
## 1952 3.2 3.1 2.9 2.9 3.0 3.0 3.2 3.4 3.1 3.0 2.8 2.7
## 1953 2.9 2.6 2.6 2.7 2.5 2.5 2.6 2.7 2.9 3.1 3.5 4.5
## 1954 4.9 5.2 5.7 5.9 5.9 5.6 5.8 6.0 6.1 5.7 5.3 5.0
## 1955 4.9 4.7 4.6 4.7 4.3 4.2 4.0 4.2 4.1 4.3 4.2 4.2
## 1956 4.0 3.9 4.2 4.0 4.3 4.3 4.4 4.1 3.9 3.9 4.3 4.2
## 1957 4.2 3.9 3.7 3.9 4.1 4.3 4.2 4.1 4.4 4.5 5.1 5.2
## 1958 5.8 6.4 6.7 7.4 7.4 7.3 7.5 7.4 7.1 6.7 6.2 6.2
## 1959 6.0 5.9 5.6 5.2 5.1 5.0 5.1 5.2 5.5 5.7 5.8 5.3
## 1960 5.2 4.8 5.4 5.2 5.1 5.4 5.5 5.6 5.5 6.1 6.1 6.6
## 1961 6.6 6.9 6.9 7.0 7.1 6.9 7.0 6.6 6.7 6.5 6.1 6.0
## 1962 5.8 5.5 5.6 5.6 5.5 5.5 5.4 5.7 5.6 5.4 5.7 5.5
## 1963 5.7 5.9 5.7 5.7 5.9 5.6 5.6 5.4 5.5 5.5 5.7 5.5
## 1964 5.6 5.4 5.4 5.3 5.1 5.2 4.9 5.0 5.1 5.1 4.8 5.0
## 1965 4.9 5.1 4.7 4.8 4.6 4.6 4.4 4.4 4.3 4.2 4.1 4.0
## 1966 4.0 3.8 3.8 3.8 3.9 3.8 3.8 3.8 3.7 3.7 3.6 3.8
## 1967 3.9 3.8 3.8 3.8 3.8 3.9 3.8 3.8 3.8 4.0 3.9 3.8
## 1968 3.7 3.8 3.7 3.5 3.5 3.7 3.7 3.5 3.4 3.4 3.4 3.4
## 1969 3.4 3.4 3.4 3.4 3.4 3.5 3.5 3.5 3.7 3.7 3.5 3.5
## 1970 3.9 4.2 4.4 4.6 4.8 4.9 5.0 5.1 5.4 5.5 5.9 6.1
## 1971 5.9 5.9 6.0 5.9 5.9 5.9 6.0 6.1 6.0 5.8 6.0 6.0
## 1972 5.8 5.7 5.8 5.7 5.7 5.7 5.6 5.6 5.5 5.6 5.3 5.2
## 1973 4.9 5.0 4.9 5.0 4.9 4.9 4.8 4.8 4.8 4.6 4.8 4.9
## 1974 5.1 5.2 5.1 5.1 5.1 5.4 5.5 5.5 5.9 6.0 6.6 7.2
## 1975 8.1 8.1 8.6 8.8 9.0 8.8 8.6 8.4 8.4 8.4 8.3 8.2
## 1976 7.9 7.7 7.6 7.7 7.4 7.6 7.8 7.8 7.6 7.7 7.8 7.8
## 1977 7.5 7.6 7.4 7.2 7.0 7.2 6.9 7.0 6.8 6.8 6.8 6.4
## 1978 6.4 6.3 6.3 6.1 6.0 5.9 6.2 5.9 6.0 5.8 5.9 6.0
## 1979 5.9 5.9 5.8 5.8 5.6 5.7 5.7 6.0 5.9 6.0 5.9 6.0
## 1980 6.3 6.3 6.3 6.9 7.5 7.6 7.8 7.7 7.5 7.5 7.5 7.2
## 1981 7.5 7.4 7.4 7.2 7.5 7.5 7.2 7.4 7.6 7.9 8.3 8.5
## 1982 8.6 8.9 9.0 9.3 9.4 9.6 9.8 9.8 10.1 10.4 10.8 10.8
## 1983 10.4 10.4 10.3 10.2 10.1 10.1 9.4 9.5 9.2 8.8 8.5 8.3
## 1984 8.0 7.8 7.8 7.7 7.4 7.2 7.5 7.5 7.3 7.4 7.2 7.3
## 1985 7.3 7.2 7.2 7.3 7.2 7.4 7.4 7.1 7.1 7.1 7.0 7.0
## 1986 6.7 7.2 7.2 7.1 7.2 7.2 7.0 6.9 7.0 7.0 6.9 6.6
## 1987 6.6 6.6 6.6 6.3 6.3 6.2 6.1 6.0 5.9 6.0 5.8 5.7
## 1988 5.7 5.7 5.7 5.4 5.6 5.4 5.4 5.6 5.4 5.4 5.3 5.3
## 1989 5.4 5.2 5.0 5.2 5.2 5.3 5.2 5.2 5.3 5.3 5.4 5.4
## 1990 5.4 5.3 5.2 5.4 5.4 5.2 5.5 5.7 5.9 5.9 6.2 6.3
## 1991 6.4 6.6 6.8 6.7 6.9 6.9 6.8 6.9 6.9 7.0 7.0 7.3
## 1992 7.3 7.4 7.4 7.4 7.6 7.8 7.7 7.6 7.6 7.3 7.4 7.4
## 1993 7.3 7.1 7.0 7.1 7.1 7.0 6.9 6.8 6.7 6.8 6.6 6.5
## 1994 6.6 6.6 6.5 6.4 6.1 6.1 6.1 6.0 5.9 5.8 5.6 5.5
## 1995 5.6 5.4 5.4 5.8 5.6 5.6 5.7 5.7 5.6 5.5 5.6 5.6
## 1996 5.6 5.5 5.5 5.6 5.6 5.3 5.5 5.1 5.2 5.2 5.4 5.4
## 1997 5.3 5.2 5.2 5.1 4.9 5.0 4.9 4.8 4.9 4.7 4.6 4.7
## 1998 4.6 4.6 4.7 4.3 4.4 4.5 4.5 4.5 4.6 4.5 4.4 4.4
## 1999 4.3 4.4 4.2 4.3 4.2 4.3 4.3 4.2 4.2 4.1 4.1 4.0
## 2000 4.0 4.1 4.0 3.8 4.0 4.0 4.0 4.1 3.9 3.9 3.9 3.9
## 2001 4.2 4.2 4.3 4.4 4.3 4.5 4.6 4.9 5.0 5.3 5.5 5.7
## 2002 5.7 5.7 5.7 5.9 5.8 5.8 5.8 5.7 5.7 5.7 5.9 6.0
## 2003 5.8 5.9 5.9 6.0 6.1 6.3 6.2 6.1 6.1 6.0 5.8 5.7
## 2004 5.7 5.6 5.8 5.6 5.6 5.6 5.5 5.4 5.4 5.5 5.4 5.4
## 2005 5.3 5.4 5.2 5.2 5.1 5.0 5.0 4.9 5.0 5.0 5.0 4.9
## 2006 4.7 4.8 4.7 4.7 4.6 4.6 4.7 4.7 4.5 4.4 4.5 4.4
## 2007 4.6 4.5 4.4 4.5 4.4 4.6 4.7 4.6 4.7 4.7 4.7 5.0
## 2008 5.0 4.9 5.1 5.0 5.4 5.6 5.8 6.1 6.1 6.5 6.8 7.3
## 2009 7.8 8.3 8.7 9.0 9.4 9.5 9.5 9.6 9.8 10.0 9.9 9.9
## 2010 9.8 9.8 9.9 9.9 9.6 9.4 9.4 9.5 9.5 9.4 9.8 9.3
## 2011 9.1 9.0 9.0 9.1 9.0 9.1 9.0 9.0 9.0 8.8 8.6 8.5
## 2012 8.3 8.3 8.2 8.2 8.2 8.2 8.2 8.1 7.8 7.8 7.7 7.9
## 2013 8.0 7.7 7.5 7.6 7.5 7.5 7.3 7.3 7.2 7.2 6.9 6.7
## 2014 6.6 6.7 6.7 6.2 6.3 6.1 6.2 6.2 5.9 5.7 5.8 5.6
## 2015 5.7 5.5 5.4 5.4 5.5 5.3 5.2 5.1 5.0 5.0 5.0 5.0
## 2016 4.9 4.9 5.0 5.0 4.7 4.9 4.9 4.9 4.9 4.8 4.6 4.7
## 2017 4.8 4.7 4.5 4.4 4.3 4.4 4.3 4.4 4.2
##
## $seasonal
## Jan Feb Mar Apr May
## 1948 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1949 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1950 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1951 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1952 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1953 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1954 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1955 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1956 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1957 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1958 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1959 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1960 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1961 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1962 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1963 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1964 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1965 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1966 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1967 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1968 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1969 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1970 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1971 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1972 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1973 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1974 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1975 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1976 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1977 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1978 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1979 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1980 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1981 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1982 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1983 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1984 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1985 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1986 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1987 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1988 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1989 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1990 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1991 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1992 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1993 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1994 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1995 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1996 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1997 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1998 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 1999 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2000 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2001 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2002 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2003 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2004 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2005 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2006 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2007 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2008 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2009 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2010 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2011 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2012 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2013 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2014 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2015 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2016 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## 2017 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## Jun Jul Aug Sep Oct
## 1948 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1949 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1950 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1951 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1952 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1953 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1954 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1955 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1956 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1957 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1958 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1959 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1960 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1961 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1962 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1963 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1964 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1965 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1966 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1967 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1968 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1969 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1970 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1971 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1972 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1973 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1974 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1975 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1976 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1977 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1978 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1979 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1980 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1981 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1982 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1983 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1984 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1985 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1986 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1987 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1988 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1989 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1990 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1991 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1992 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1993 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1994 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1995 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1996 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1997 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1998 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 1999 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2000 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2001 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2002 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2003 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2004 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2005 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2006 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2007 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2008 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2009 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2010 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2011 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2012 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2013 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2014 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2015 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2016 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## 2017 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618
## Nov Dec
## 1948 -0.0081521739 -0.0004227053
## 1949 -0.0081521739 -0.0004227053
## 1950 -0.0081521739 -0.0004227053
## 1951 -0.0081521739 -0.0004227053
## 1952 -0.0081521739 -0.0004227053
## 1953 -0.0081521739 -0.0004227053
## 1954 -0.0081521739 -0.0004227053
## 1955 -0.0081521739 -0.0004227053
## 1956 -0.0081521739 -0.0004227053
## 1957 -0.0081521739 -0.0004227053
## 1958 -0.0081521739 -0.0004227053
## 1959 -0.0081521739 -0.0004227053
## 1960 -0.0081521739 -0.0004227053
## 1961 -0.0081521739 -0.0004227053
## 1962 -0.0081521739 -0.0004227053
## 1963 -0.0081521739 -0.0004227053
## 1964 -0.0081521739 -0.0004227053
## 1965 -0.0081521739 -0.0004227053
## 1966 -0.0081521739 -0.0004227053
## 1967 -0.0081521739 -0.0004227053
## 1968 -0.0081521739 -0.0004227053
## 1969 -0.0081521739 -0.0004227053
## 1970 -0.0081521739 -0.0004227053
## 1971 -0.0081521739 -0.0004227053
## 1972 -0.0081521739 -0.0004227053
## 1973 -0.0081521739 -0.0004227053
## 1974 -0.0081521739 -0.0004227053
## 1975 -0.0081521739 -0.0004227053
## 1976 -0.0081521739 -0.0004227053
## 1977 -0.0081521739 -0.0004227053
## 1978 -0.0081521739 -0.0004227053
## 1979 -0.0081521739 -0.0004227053
## 1980 -0.0081521739 -0.0004227053
## 1981 -0.0081521739 -0.0004227053
## 1982 -0.0081521739 -0.0004227053
## 1983 -0.0081521739 -0.0004227053
## 1984 -0.0081521739 -0.0004227053
## 1985 -0.0081521739 -0.0004227053
## 1986 -0.0081521739 -0.0004227053
## 1987 -0.0081521739 -0.0004227053
## 1988 -0.0081521739 -0.0004227053
## 1989 -0.0081521739 -0.0004227053
## 1990 -0.0081521739 -0.0004227053
## 1991 -0.0081521739 -0.0004227053
## 1992 -0.0081521739 -0.0004227053
## 1993 -0.0081521739 -0.0004227053
## 1994 -0.0081521739 -0.0004227053
## 1995 -0.0081521739 -0.0004227053
## 1996 -0.0081521739 -0.0004227053
## 1997 -0.0081521739 -0.0004227053
## 1998 -0.0081521739 -0.0004227053
## 1999 -0.0081521739 -0.0004227053
## 2000 -0.0081521739 -0.0004227053
## 2001 -0.0081521739 -0.0004227053
## 2002 -0.0081521739 -0.0004227053
## 2003 -0.0081521739 -0.0004227053
## 2004 -0.0081521739 -0.0004227053
## 2005 -0.0081521739 -0.0004227053
## 2006 -0.0081521739 -0.0004227053
## 2007 -0.0081521739 -0.0004227053
## 2008 -0.0081521739 -0.0004227053
## 2009 -0.0081521739 -0.0004227053
## 2010 -0.0081521739 -0.0004227053
## 2011 -0.0081521739 -0.0004227053
## 2012 -0.0081521739 -0.0004227053
## 2013 -0.0081521739 -0.0004227053
## 2014 -0.0081521739 -0.0004227053
## 2015 -0.0081521739 -0.0004227053
## 2016 -0.0081521739 -0.0004227053
## 2017
##
## $trend
## Jan Feb Mar Apr May Jun Jul
## 1948 NA NA NA NA NA NA 3.787500
## 1949 4.662500 4.912500 5.150000 5.441667 5.725000 5.941667 6.141667
## 1950 6.337500 6.170833 5.983333 5.737500 5.491667 5.304167 5.091667
## 1951 3.787500 3.650000 3.545833 3.470833 3.412500 3.333333 3.262500
## 1952 3.145833 3.162500 3.166667 3.137500 3.087500 3.041667 3.012500
## 1953 2.808333 2.754167 2.716667 2.712500 2.745833 2.850000 3.008333
## 1954 4.508333 4.779167 5.050000 5.291667 5.475000 5.570833 5.591667
## 1955 5.033333 4.883333 4.725000 4.583333 4.479167 4.400000 4.329167
## 1956 4.158333 4.170833 4.158333 4.133333 4.120833 4.125000 4.133333
## 1957 4.066667 4.058333 4.079167 4.125000 4.183333 4.258333 4.366667
## 1958 5.845833 6.120833 6.370833 6.575000 6.712500 6.800000 6.850000
## 1959 6.058333 5.866667 5.708333 5.600000 5.541667 5.487500 5.416667
## 1960 5.325000 5.358333 5.375000 5.391667 5.420833 5.487500 5.600000
## 1961 6.462500 6.566667 6.658333 6.725000 6.741667 6.716667 6.658333
## 1962 5.966667 5.862500 5.779167 5.687500 5.625000 5.587500 5.562500
## 1963 5.658333 5.654167 5.637500 5.637500 5.641667 5.641667 5.637500
## 1964 5.404167 5.358333 5.325000 5.291667 5.237500 5.179167 5.129167
## 1965 4.862500 4.816667 4.758333 4.687500 4.620833 4.550000 4.470833
## 1966 4.016667 3.966667 3.916667 3.870833 3.829167 3.800000 3.787500
## 1967 3.783333 3.783333 3.787500 3.804167 3.829167 3.841667 3.833333
## 1968 3.745833 3.729167 3.700000 3.658333 3.612500 3.575000 3.545833
## 1969 3.433333 3.425000 3.437500 3.462500 3.479167 3.487500 3.512500
## 1970 4.079167 4.208333 4.345833 4.491667 4.666667 4.875000 5.066667
## 1971 5.750000 5.833333 5.900000 5.937500 5.954167 5.954167 5.945833
## 1972 5.841667 5.804167 5.762500 5.733333 5.695833 5.633333 5.562500
## 1973 5.166667 5.100000 5.037500 4.966667 4.904167 4.870833 4.866667
## 1974 5.004167 5.062500 5.137500 5.241667 5.375000 5.545833 5.766667
## 1975 7.470833 7.720833 7.945833 8.150000 8.320833 8.433333 8.466667
## 1976 7.983333 7.925000 7.866667 7.804167 7.754167 7.716667 7.683333
## 1977 7.495833 7.425000 7.358333 7.287500 7.208333 7.108333 7.004167
## 1978 6.445833 6.370833 6.291667 6.216667 6.137500 6.083333 6.045833
## 1979 5.854167 5.837500 5.837500 5.841667 5.850000 5.850000 5.866667
## 1980 6.454167 6.612500 6.750000 6.879167 7.008333 7.125000 7.225000
## 1981 7.450000 7.412500 7.404167 7.425000 7.475000 7.562500 7.662500
## 1982 8.583333 8.791667 8.995833 9.204167 9.412500 9.612500 9.783333
## 1983 10.250000 10.220833 10.170833 10.066667 9.904167 9.704167 9.500000
## 1984 8.220833 8.058333 7.895833 7.758333 7.645833 7.550000 7.479167
## 1985 7.312500 7.291667 7.266667 7.245833 7.225000 7.204167 7.166667
## 1986 7.091667 7.066667 7.054167 7.045833 7.037500 7.016667 6.995833
## 1987 6.629167 6.554167 6.470833 6.383333 6.295833 6.212500 6.137500
## 1988 5.720833 5.675000 5.637500 5.591667 5.545833 5.508333 5.479167
## 1989 5.300000 5.275000 5.254167 5.245833 5.245833 5.254167 5.258333
## 1990 5.320833 5.354167 5.400000 5.450000 5.508333 5.579167 5.658333
## 1991 6.370833 6.475000 6.566667 6.654167 6.733333 6.808333 6.887500
## 1992 7.270833 7.337500 7.395833 7.437500 7.466667 7.487500 7.491667
## 1993 7.266667 7.200000 7.129167 7.070833 7.016667 6.945833 6.879167
## 1994 6.516667 6.450000 6.383333 6.308333 6.225000 6.141667 6.058333
## 1995 5.675000 5.645833 5.620833 5.595833 5.583333 5.587500 5.591667
## 1996 5.558333 5.525000 5.483333 5.454167 5.433333 5.416667 5.395833
## 1997 5.183333 5.145833 5.120833 5.087500 5.033333 4.970833 4.912500
## 1998 4.625000 4.595833 4.570833 4.550000 4.533333 4.512500 4.487500
## 1999 4.375000 4.354167 4.325000 4.291667 4.262500 4.233333 4.204167
## 2000 4.054167 4.037500 4.020833 4.000000 3.983333 3.970833 3.975000
## 2001 4.158333 4.216667 4.295833 4.400000 4.525000 4.666667 4.804167
## 2002 5.516667 5.600000 5.662500 5.708333 5.741667 5.770833 5.787500
## 2003 5.916667 5.950000 5.983333 6.012500 6.020833 6.004167 5.987500
## 2004 5.787500 5.729167 5.670833 5.620833 5.583333 5.554167 5.525000
## 2005 5.295833 5.254167 5.216667 5.179167 5.141667 5.104167 5.058333
## 2006 4.812500 4.791667 4.762500 4.716667 4.670833 4.629167 4.604167
## 2007 4.516667 4.512500 4.516667 4.537500 4.558333 4.591667 4.633333
## 2008 4.995833 5.104167 5.225000 5.358333 5.520833 5.704167 5.916667
## 2009 7.762500 8.062500 8.362500 8.662500 8.937500 9.175000 9.366667
## 2010 9.754167 9.745833 9.729167 9.691667 9.662500 9.633333 9.579167
## 2011 9.250000 9.212500 9.170833 9.125000 9.050000 8.966667 8.900000
## 2012 8.491667 8.420833 8.333333 8.241667 8.162500 8.100000 8.062500
## 2013 7.737500 7.666667 7.608333 7.558333 7.500000 7.416667 7.308333
## 2014 6.720833 6.629167 6.529167 6.412500 6.304167 6.212500 6.129167
## 2015 5.641667 5.554167 5.470833 5.404167 5.341667 5.283333 5.225000
## 2016 4.962500 4.941667 4.929167 4.916667 4.891667 4.862500 4.845833
## 2017 4.633333 4.587500 4.537500 NA NA NA NA
## Aug Sep Oct Nov Dec
## 1948 3.862500 3.941667 4.041667 4.208333 4.425000
## 1949 6.304167 6.429167 6.504167 6.500000 6.441667
## 1950 4.850000 4.604167 4.370833 4.154167 3.958333
## 1951 3.229167 3.195833 3.166667 3.158333 3.150000
## 1952 2.979167 2.945833 2.925000 2.895833 2.854167
## 1953 3.200000 3.437500 3.700000 3.975000 4.245833
## 1954 5.570833 5.504167 5.408333 5.291667 5.166667
## 1955 4.258333 4.208333 4.162500 4.133333 4.137500
## 1956 4.141667 4.120833 4.095833 4.083333 4.075000
## 1957 4.537500 4.766667 5.037500 5.320833 5.583333
## 1958 6.837500 6.770833 6.633333 6.445833 6.254167
## 1959 5.337500 5.283333 5.275000 5.275000 5.291667
## 1960 5.745833 5.895833 6.033333 6.191667 6.337500
## 1961 6.566667 6.454167 6.341667 6.216667 6.091667
## 1962 5.575000 5.595833 5.604167 5.625000 5.645833
## 1963 5.612500 5.579167 5.550000 5.500000 5.450000
## 1964 5.087500 5.045833 4.995833 4.954167 4.908333
## 1965 4.379167 4.287500 4.208333 4.137500 4.075000
## 1966 3.783333 3.783333 3.783333 3.779167 3.779167
## 1967 3.825000 3.820833 3.804167 3.779167 3.758333
## 1968 3.516667 3.487500 3.470833 3.462500 3.450000
## 1969 3.566667 3.641667 3.733333 3.841667 3.958333
## 1970 5.220833 5.358333 5.479167 5.579167 5.666667
## 1971 5.933333 5.916667 5.900000 5.883333 5.866667
## 1972 5.495833 5.429167 5.362500 5.300000 5.233333
## 1973 4.883333 4.900000 4.912500 4.925000 4.954167
## 1974 6.012500 6.279167 6.579167 6.895833 7.200000
## 1975 8.441667 8.383333 8.295833 8.183333 8.066667
## 1976 7.662500 7.650000 7.620833 7.583333 7.550000
## 1977 6.904167 6.804167 6.712500 6.625000 6.529167
## 1978 6.008333 5.970833 5.937500 5.908333 5.883333
## 1979 5.900000 5.937500 6.004167 6.129167 6.287500
## 1980 7.320833 7.412500 7.470833 7.483333 7.479167
## 1981 7.770833 7.900000 8.054167 8.220833 8.387500
## 1982 9.920833 10.037500 10.129167 10.195833 10.245833
## 1983 9.291667 9.079167 8.870833 8.654167 8.420833
## 1984 7.425000 7.375000 7.333333 7.308333 7.308333
## 1985 7.141667 7.141667 7.133333 7.125000 7.116667
## 1986 6.966667 6.916667 6.858333 6.787500 6.708333
## 1987 6.062500 5.987500 5.912500 5.845833 5.783333
## 1988 5.445833 5.395833 5.358333 5.333333 5.312500
## 1989 5.262500 5.275000 5.291667 5.308333 5.312500
## 1990 5.754167 5.875000 5.995833 6.112500 6.245833
## 1991 6.958333 7.016667 7.070833 7.129167 7.195833
## 1992 7.479167 7.450000 7.420833 7.387500 7.333333
## 1993 6.829167 6.787500 6.737500 6.666667 6.587500
## 1994 5.966667 5.870833 5.800000 5.754167 5.712500
## 1995 5.595833 5.604167 5.600000 5.591667 5.579167
## 1996 5.370833 5.345833 5.312500 5.262500 5.220833
## 1997 4.858333 4.812500 4.758333 4.704167 4.662500
## 1998 4.466667 4.437500 4.416667 4.408333 4.391667
## 1999 4.179167 4.158333 4.129167 4.100000 4.079167
## 2000 3.987500 4.004167 4.041667 4.079167 4.112500
## 2001 4.929167 5.050000 5.170833 5.295833 5.412500
## 2002 5.800000 5.816667 5.829167 5.845833 5.879167
## 2003 5.970833 5.954167 5.933333 5.895833 5.845833
## 2004 5.500000 5.466667 5.425000 5.387500 5.341667
## 2005 5.008333 4.962500 4.920833 4.879167 4.841667
## 2006 4.587500 4.562500 4.541667 4.525000 4.516667
## 2007 4.666667 4.712500 4.762500 4.825000 4.908333
## 2008 6.175000 6.466667 6.783333 7.116667 7.445833
## 2009 9.512500 9.625000 9.712500 9.758333 9.762500
## 2010 9.516667 9.445833 9.375000 9.316667 9.279167
## 2011 8.837500 8.775000 8.704167 8.633333 8.562500
## 2012 8.025000 7.970833 7.916667 7.862500 7.804167
## 2013 7.208333 7.133333 7.041667 6.933333 6.825000
## 2014 6.041667 5.937500 5.850000 5.783333 5.716667
## 2015 5.166667 5.125000 5.091667 5.041667 4.991667
## 2016 4.833333 4.804167 4.758333 4.716667 4.679167
## 2017 NA NA
##
## $random
## Jan Feb Mar Apr May
## 1948 NA NA NA NA NA
## 1949 -0.3640700483 -0.2060990338 -0.1488526570 -0.1426568272 0.3737034669
## 1950 0.1609299517 0.2355676329 0.3178140097 0.0615098394 0.0070368002
## 1951 -0.0890700483 -0.2435990338 -0.1446859903 -0.3718234939 -0.4137965331
## 1952 0.0525966184 -0.0560990338 -0.2655193237 -0.2384901606 -0.0887965331
## 1953 0.0900966184 -0.1477657005 -0.1155193237 -0.0134901606 -0.2471298664
## 1954 0.3900966184 0.4272342995 0.6511473430 0.6073431728 0.4237034669
## 1955 -0.1349033816 -0.1769323671 -0.1238526570 0.1156765061 -0.1804631998
## 1956 -0.1599033816 -0.2644323671 0.0428140097 -0.1343234939 0.1778701336
## 1957 0.1317632850 -0.1519323671 -0.3780193237 -0.2259901606 -0.0846298664
## 1958 -0.0474033816 0.2855676329 0.3303140097 0.8240098394 0.6862034669
## 1959 -0.0599033816 0.0397342995 -0.1071859903 -0.4009901606 -0.4429631998
## 1960 -0.1265700483 -0.5519323671 0.0261473430 -0.1926568272 -0.3221298664
## 1961 0.1359299517 0.3397342995 0.2428140097 0.2740098394 0.3570368002
## 1962 -0.1682367150 -0.3560990338 -0.1780193237 -0.0884901606 -0.1262965331
## 1963 0.0400966184 0.2522342995 0.0636473430 0.0615098394 0.2570368002
## 1964 0.1942632850 0.0480676329 0.0761473430 0.0073431728 -0.1387965331
## 1965 0.0359299517 0.2897342995 -0.0571859903 0.1115098394 -0.0221298664
## 1966 -0.0182367150 -0.1602657005 -0.1155193237 -0.0718234939 0.0695368002
## 1967 0.1150966184 0.0230676329 0.0136473430 -0.0051568272 -0.0304631998
## 1968 -0.0474033816 0.0772342995 0.0011473430 -0.1593234939 -0.1137965331
## 1969 -0.0349033816 -0.0185990338 -0.0363526570 -0.0634901606 -0.0804631998
## 1970 -0.1807367150 -0.0019323671 0.0553140097 0.1073431728 0.1320368002
## 1971 0.1484299517 0.0730676329 0.1011473430 -0.0384901606 -0.0554631998
## 1972 -0.0432367150 -0.0977657005 0.0386473430 -0.0343234939 0.0028701336
## 1973 -0.2682367150 -0.0935990338 -0.1363526570 0.0323431728 -0.0054631998
## 1974 0.0942632850 0.1439009662 -0.0363526570 -0.1426568272 -0.2762965331
## 1975 0.6275966184 0.3855676329 0.6553140097 0.6490098394 0.6778701336
## 1976 -0.0849033816 -0.2185990338 -0.2655193237 -0.1051568272 -0.3554631998
## 1977 0.0025966184 0.1814009662 0.0428140097 -0.0884901606 -0.2096298664
## 1978 -0.0474033816 -0.0644323671 0.0094806763 -0.1176568272 -0.1387965331
## 1979 0.0442632850 0.0689009662 -0.0363526570 -0.0426568272 -0.2512965331
## 1980 -0.1557367150 -0.3060990338 -0.4488526570 0.0198431728 0.4903701336
## 1981 0.0484299517 -0.0060990338 -0.0030193237 -0.2259901606 0.0237034669
## 1982 0.0150966184 0.1147342995 0.0053140097 0.0948431728 -0.0137965331
## 1983 0.1484299517 0.1855676329 0.1303140097 0.1323431728 0.1945368002
## 1984 -0.2224033816 -0.2519323671 -0.0946859903 -0.0593234939 -0.2471298664
## 1985 -0.0140700483 -0.0852657005 -0.0655193237 0.0531765061 -0.0262965331
## 1986 -0.3932367150 0.1397342995 0.1469806763 0.0531765061 0.1612034669
## 1987 -0.0307367150 0.0522342995 0.1303140097 -0.0843234939 0.0028701336
## 1988 -0.0224033816 0.0314009662 0.0636473430 -0.1926568272 0.0528701336
## 1989 0.0984299517 -0.0685990338 -0.2530193237 -0.0468234939 -0.0471298664
## 1990 0.0775966184 -0.0477657005 -0.1988526570 -0.0509901606 -0.1096298664
## 1991 0.0275966184 0.1314009662 0.2344806763 0.0448431728 0.1653701336
## 1992 0.0275966184 0.0689009662 0.0053140097 -0.0384901606 0.1320368002
## 1993 0.0317632850 -0.0935990338 -0.1280193237 0.0281765061 0.0820368002
## 1994 0.0817632850 0.1564009662 0.1178140097 0.0906765061 -0.1262965331
## 1995 -0.0765700483 -0.2394323671 -0.2196859903 0.2031765061 0.0153701336
## 1996 0.0400966184 -0.0185990338 0.0178140097 0.1448431728 0.1653701336
## 1997 0.1150966184 0.0605676329 0.0803140097 0.0115098394 -0.1346298664
## 1998 -0.0265700483 0.0105676329 0.1303140097 -0.2509901606 -0.1346298664
## 1999 -0.0765700483 0.0522342995 -0.1238526570 0.0073431728 -0.0637965331
## 2000 -0.0557367150 0.0689009662 -0.0196859903 -0.2009901606 0.0153701336
## 2001 0.0400966184 -0.0102657005 0.0053140097 -0.0009901606 -0.2262965331
## 2002 0.1817632850 0.1064009662 0.0386473430 0.1906765061 0.0570368002
## 2003 -0.1182367150 -0.0435990338 -0.0821859903 -0.0134901606 0.0778701336
## 2004 -0.0890700483 -0.1227657005 0.1303140097 -0.0218234939 0.0153701336
## 2005 0.0025966184 0.1522342995 -0.0155193237 0.0198431728 -0.0429631998
## 2006 -0.1140700483 0.0147342995 -0.0613526570 -0.0176568272 -0.0721298664
## 2007 0.0817632850 -0.0060990338 -0.1155193237 -0.0384901606 -0.1596298664
## 2008 0.0025966184 -0.1977657005 -0.1238526570 -0.3593234939 -0.1221298664
## 2009 0.0359299517 0.2439009662 0.3386473430 0.3365098394 0.4612034669
## 2010 0.0442632850 0.0605676329 0.1719806763 0.2073431728 -0.0637965331
## 2011 -0.1515700483 -0.2060990338 -0.1696859903 -0.0259901606 -0.0512965331
## 2012 -0.1932367150 -0.1144323671 -0.1321859903 -0.0426568272 0.0362034669
## 2013 0.2609299517 0.0397342995 -0.1071859903 0.0406765061 -0.0012965331
## 2014 -0.1224033816 0.0772342995 0.1719806763 -0.2134901606 -0.0054631998
## 2015 0.0567632850 -0.0477657005 -0.0696859903 -0.0051568272 0.1570368002
## 2016 -0.0640700483 -0.0352657005 0.0719806763 0.0823431728 -0.1929631998
## 2017 0.1650966184 0.1189009662 -0.0363526570 NA NA
## Jun Jul Aug Sep Oct
## 1948 NA -0.1960144928 0.0376207729 -0.1276570048 -0.3429951691
## 1949 0.2417794473 0.5498188406 0.4959541063 0.1848429952 1.3945048309
## 1950 0.0792794473 -0.1001811594 -0.3498792271 -0.1901570048 -0.1721618357
## 1951 -0.1498872194 -0.1710144928 -0.1290458937 0.1181763285 0.3320048309
## 1952 -0.0582205527 0.1789855072 0.4209541063 0.1681763285 0.0736714976
## 1953 -0.3665538860 -0.4168478261 -0.4998792271 -0.5234903382 -0.6013285024
## 1954 0.0126127806 0.1998188406 0.4292874396 0.6098429952 0.2903381643
## 1955 -0.2165538860 -0.3376811594 -0.0582125604 -0.0943236715 0.1361714976
## 1956 0.1584461140 0.2581521739 -0.0415458937 -0.2068236715 -0.1971618357
## 1957 0.0251127806 -0.1751811594 -0.4373792271 -0.3526570048 -0.5388285024
## 1958 0.4834461140 0.6414855072 0.5626207729 0.3431763285 0.0653381643
## 1959 -0.5040538860 -0.3251811594 -0.1373792271 0.2306763285 0.4236714976
## 1960 -0.1040538860 -0.1085144928 -0.1457125604 -0.3818236715 0.0653381643
## 1961 0.1667794473 0.3331521739 0.0334541063 0.2598429952 0.1570048309
## 1962 -0.1040538860 -0.1710144928 0.1251207729 0.0181763285 -0.2054951691
## 1963 -0.0582205527 -0.0460144928 -0.2123792271 -0.0651570048 -0.0513285024
## 1964 0.0042794473 -0.2376811594 -0.0873792271 0.0681763285 0.1028381643
## 1965 0.0334461140 -0.0793478261 0.0209541063 0.0265096618 -0.0096618357
## 1966 -0.0165538860 0.0039855072 0.0167874396 -0.0693236715 -0.0846618357
## 1967 0.0417794473 -0.0418478261 -0.0248792271 -0.0068236715 0.1945048309
## 1968 0.1084461140 0.1456521739 -0.0165458937 -0.0734903382 -0.0721618357
## 1969 -0.0040538860 -0.0210144928 -0.0665458937 0.0723429952 -0.0346618357
## 1970 0.0084461140 -0.0751811594 -0.1207125604 0.0556763285 0.0195048309
## 1971 -0.0707205527 0.0456521739 0.1667874396 0.0973429952 -0.1013285024
## 1972 0.0501127806 0.0289855072 0.1042874396 0.0848429952 0.2361714976
## 1973 0.0126127806 -0.0751811594 -0.0832125604 -0.0859903382 -0.3138285024
## 1974 -0.1623872194 -0.2751811594 -0.5123792271 -0.3651570048 -0.5804951691
## 1975 0.3501127806 0.1248188406 -0.0415458937 0.0306763285 0.1028381643
## 1976 -0.1332205527 0.1081521739 0.1376207729 -0.0359903382 0.0778381643
## 1977 0.0751127806 -0.1126811594 0.0959541063 0.0098429952 0.0861714976
## 1978 -0.1998872194 0.1456521739 -0.1082125604 0.0431763285 -0.1388285024
## 1979 -0.1665538860 -0.1751811594 0.1001207729 -0.0234903382 -0.0054951691
## 1980 0.4584461140 0.5664855072 0.3792874396 0.1015096618 0.0278381643
## 1981 -0.0790538860 -0.4710144928 -0.3707125604 -0.2859903382 -0.1554951691
## 1982 -0.0290538860 0.0081521739 -0.1207125604 0.0765096618 0.2695048309
## 1983 0.3792794473 -0.1085144928 0.2084541063 0.1348429952 -0.0721618357
## 1984 -0.3665538860 0.0123188406 0.0751207729 -0.0609903382 0.0653381643
## 1985 0.1792794473 0.2248188406 -0.0415458937 -0.0276570048 -0.0346618357
## 1986 0.1667794473 -0.0043478261 -0.0665458937 0.0973429952 0.1403381643
## 1987 -0.0290538860 -0.0460144928 -0.0623792271 -0.0734903382 0.0861714976
## 1988 -0.1248872194 -0.0876811594 0.1542874396 0.0181763285 0.0403381643
## 1989 0.0292794473 -0.0668478261 -0.0623792271 0.0390096618 0.0070048309
## 1990 -0.3957205527 -0.1668478261 -0.0540458937 0.0390096618 -0.0971618357
## 1991 0.0751127806 -0.0960144928 -0.0582125604 -0.1026570048 -0.0721618357
## 1992 0.2959461140 0.1998188406 0.1209541063 0.1640096618 -0.1221618357
## 1993 0.0376127806 0.0123188406 -0.0290458937 -0.0734903382 0.0611714976
## 1994 -0.0582205527 0.0331521739 0.0334541063 0.0431763285 -0.0013285024
## 1995 -0.0040538860 0.0998188406 0.1042874396 0.0098429952 -0.1013285024
## 1996 -0.1332205527 0.0956521739 -0.2707125604 -0.1318236715 -0.1138285024
## 1997 0.0126127806 -0.0210144928 -0.0582125604 0.1015096618 -0.0596618357
## 1998 -0.0290538860 0.0039855072 0.0334541063 0.1765096618 0.0820048309
## 1999 0.0501127806 0.0873188406 0.0209541063 0.0556763285 -0.0304951691
## 2000 0.0126127806 0.0164855072 0.1126207729 -0.0901570048 -0.1429951691
## 2001 -0.1832205527 -0.2126811594 -0.0290458937 -0.0359903382 0.1278381643
## 2002 0.0126127806 0.0039855072 -0.0998792271 -0.1026570048 -0.1304951691
## 2003 0.2792794473 0.2039855072 0.1292874396 0.1598429952 0.0653381643
## 2004 0.0292794473 -0.0335144928 -0.0998792271 -0.0526570048 0.0736714976
## 2005 -0.1207205527 -0.0668478261 -0.1082125604 0.0515096618 0.0778381643
## 2006 -0.0457205527 0.0873188406 0.1126207729 -0.0484903382 -0.1429951691
## 2007 -0.0082205527 0.0581521739 -0.0665458937 0.0015096618 -0.0638285024
## 2008 -0.1207205527 -0.1251811594 -0.0748792271 -0.3526570048 -0.2846618357
## 2009 0.3084461140 0.1248188406 0.0876207729 0.1890096618 0.2861714976
## 2010 -0.2498872194 -0.1876811594 -0.0165458937 0.0681763285 0.0236714976
## 2011 0.1167794473 0.0914855072 0.1626207729 0.2390096618 0.0945048309
## 2012 0.0834461140 0.1289855072 0.0751207729 -0.1568236715 -0.1179951691
## 2013 0.0667794473 -0.0168478261 0.0917874396 0.0806763285 0.1570048309
## 2014 -0.1290538860 0.0623188406 0.1584541063 -0.0234903382 -0.1513285024
## 2015 0.0001127806 -0.0335144928 -0.0665458937 -0.1109903382 -0.0929951691
## 2016 0.0209461140 0.0456521739 0.0667874396 0.1098429952 0.0403381643
## 2017 NA NA NA NA
## Nov Dec
## 1948 -0.4001811594 -0.4245772947
## 1949 -0.0918478261 0.1587560386
## 1950 0.0539855072 0.3420893720
## 1951 0.3498188406 -0.0495772947
## 1952 -0.0876811594 -0.1537439614
## 1953 -0.4668478261 0.2545893720
## 1954 0.0164855072 -0.1662439614
## 1955 0.0748188406 0.0629227053
## 1956 0.2248188406 0.1254227053
## 1957 -0.2126811594 -0.3829106280
## 1958 -0.2376811594 -0.0537439614
## 1959 0.5331521739 0.0087560386
## 1960 -0.0835144928 0.2629227053
## 1961 -0.1085144928 -0.0912439614
## 1962 0.0831521739 -0.1454106280
## 1963 0.2081521739 0.0504227053
## 1964 -0.1460144928 0.0920893720
## 1965 -0.0293478261 -0.0745772947
## 1966 -0.1710144928 0.0212560386
## 1967 0.1289855072 0.0420893720
## 1968 -0.0543478261 -0.0495772947
## 1969 -0.3335144928 -0.4579106280
## 1970 0.3289855072 0.4337560386
## 1971 0.1248188406 0.1337560386
## 1972 0.0081521739 -0.0329106280
## 1973 -0.1168478261 -0.0537439614
## 1974 -0.2876811594 0.0004227053
## 1975 0.1248188406 0.1337560386
## 1976 0.2248188406 0.2504227053
## 1977 0.1831521739 -0.1287439614
## 1978 -0.0001811594 0.1170893720
## 1979 -0.2210144928 -0.2870772947
## 1980 0.0248188406 -0.2787439614
## 1981 0.0873188406 0.1129227053
## 1982 0.6123188406 0.5545893720
## 1983 -0.1460144928 -0.1204106280
## 1984 -0.1001811594 -0.0079106280
## 1985 -0.1168478261 -0.1162439614
## 1986 0.1206521739 -0.1079106280
## 1987 -0.0376811594 -0.0829106280
## 1988 -0.0251811594 -0.0120772947
## 1989 0.0998188406 0.0879227053
## 1990 0.0956521739 0.0545893720
## 1991 -0.1210144928 0.1045893720
## 1992 0.0206521739 0.0670893720
## 1993 -0.0585144928 -0.0870772947
## 1994 -0.1460144928 -0.2120772947
## 1995 0.0164855072 0.0212560386
## 1996 0.1456521739 0.1795893720
## 1997 -0.0960144928 0.0379227053
## 1998 -0.0001811594 0.0087560386
## 1999 0.0081521739 -0.0787439614
## 2000 -0.1710144928 -0.2120772947
## 2001 0.2123188406 0.2879227053
## 2002 0.0623188406 0.1212560386
## 2003 -0.0876811594 -0.1454106280
## 2004 0.0206521739 0.0587560386
## 2005 0.1289855072 0.0587560386
## 2006 -0.0168478261 -0.1162439614
## 2007 -0.1168478261 0.0920893720
## 2008 -0.3085144928 -0.1454106280
## 2009 0.1498188406 0.1379227053
## 2010 0.4914855072 0.0212560386
## 2011 -0.0251811594 -0.0620772947
## 2012 -0.1543478261 0.0962560386
## 2013 -0.0251811594 -0.1245772947
## 2014 0.0248188406 -0.1162439614
## 2015 -0.0335144928 0.0087560386
## 2016 -0.1085144928 0.0212560386
## 2017
##
## $figure
## [1] 0.0015700483 -0.0064009662 -0.0011473430 0.0009901606 0.0012965331
## [6] 0.0165538860 0.0085144928 -0.0001207729 -0.0140096618 0.0013285024
## [11] -0.0081521739 -0.0004227053
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"plot(decompose(URATE))
An observed time series can be decomposed into three components: the trend (long term direction), the seasonal (systematic, calendar related movements) and the irregular (unsystematic, short term fluctuations).
Inflation Rate Download from FRED Website:
library(readr)
InflationRate<-read_csv("C:/Users/senet/Desktop/CSC 463 Data Visualization Tools/R/Mini Class 5/InflationRate1.csv")## Parsed with column specification:
## cols(
## DATE = col_character(),
## Inrate = col_double()
## )Changing Inflation Rate table into Time series
class(InflationRate)## [1] "tbl_df" "tbl" "data.frame"IRate<-ts(InflationRate$Inrate,start=c(2003,1),end=c(2017,9),freq=12)
head(InflationRate)## # A tibble: 6 x 2
## DATE Inrate
## <chr> <dbl>
## 1 1/2/2003 1.64
## 2 1/3/2003 1.62
## 3 1/6/2003 1.63
## 4 1/7/2003 1.62
## 5 1/8/2003 1.71
## 6 1/9/2003 1.78head(IRate)## [1] 1.64 1.62 1.63 1.62 1.71 1.78Plotting the Inflation Rate table in time series plot
IRate## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2003 1.64 1.62 1.63 1.62 1.71 1.78 1.75 1.77 1.76 1.80 1.79 1.80
## 2004 1.79 1.78 1.72 1.78 1.80 1.82 1.81 1.85 1.80 1.81 1.81 1.84
## 2005 1.90 1.88 1.89 1.93 1.93 1.89 1.88 1.92 1.90 1.89 1.89 1.94
## 2006 1.97 1.99 1.97 1.94 1.94 1.94 1.91 1.88 1.88 1.93 1.91 1.90
## 2007 1.92 1.92 2.01 1.83 1.85 1.83 1.83 1.81 1.82 1.80 1.80 1.81
## 2008 1.85 1.83 1.80 1.82 1.83 1.81 1.80 1.82 1.77 1.80 1.79 1.77
## 2009 1.82 1.80 1.76 1.76 1.75 1.75 1.74 1.76 1.71 1.73 1.76 1.74
## 2010 1.73 1.75 1.75 1.73 1.67 1.70 1.70 1.69 1.68 1.69 1.66 1.67
## 2011 1.62 1.61 1.65 1.66 1.63 1.62 1.62 1.61 1.61 1.58 1.60 1.60
## 2012 1.58 1.57 1.59 1.61 1.61 1.59 1.59 1.61 1.62 1.59 1.57 1.58
## 2013 1.61 1.63 1.61 1.61 1.67 1.70 1.68 1.64 1.64 1.60 1.58 1.59
## 2014 1.60 1.63 1.73 1.76 1.78 1.82 1.88 1.89 1.93 1.96 1.98 1.98
## 2015 2.01 2.02 2.08 2.04 2.04 2.02 2.08 2.04 2.01 2.04 1.98 2.01
## 2016 2.00 2.07 2.08 2.17 2.17 2.19 2.16 2.14 2.19 2.24 2.22 2.22
## 2017 2.22 2.18 2.13 2.16 2.17 2.18 2.20 2.20 2.18#time(IRate)
plot(IRate)
decompose(IRate)## $x
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2003 1.64 1.62 1.63 1.62 1.71 1.78 1.75 1.77 1.76 1.80 1.79 1.80
## 2004 1.79 1.78 1.72 1.78 1.80 1.82 1.81 1.85 1.80 1.81 1.81 1.84
## 2005 1.90 1.88 1.89 1.93 1.93 1.89 1.88 1.92 1.90 1.89 1.89 1.94
## 2006 1.97 1.99 1.97 1.94 1.94 1.94 1.91 1.88 1.88 1.93 1.91 1.90
## 2007 1.92 1.92 2.01 1.83 1.85 1.83 1.83 1.81 1.82 1.80 1.80 1.81
## 2008 1.85 1.83 1.80 1.82 1.83 1.81 1.80 1.82 1.77 1.80 1.79 1.77
## 2009 1.82 1.80 1.76 1.76 1.75 1.75 1.74 1.76 1.71 1.73 1.76 1.74
## 2010 1.73 1.75 1.75 1.73 1.67 1.70 1.70 1.69 1.68 1.69 1.66 1.67
## 2011 1.62 1.61 1.65 1.66 1.63 1.62 1.62 1.61 1.61 1.58 1.60 1.60
## 2012 1.58 1.57 1.59 1.61 1.61 1.59 1.59 1.61 1.62 1.59 1.57 1.58
## 2013 1.61 1.63 1.61 1.61 1.67 1.70 1.68 1.64 1.64 1.60 1.58 1.59
## 2014 1.60 1.63 1.73 1.76 1.78 1.82 1.88 1.89 1.93 1.96 1.98 1.98
## 2015 2.01 2.02 2.08 2.04 2.04 2.02 2.08 2.04 2.01 2.04 1.98 2.01
## 2016 2.00 2.07 2.08 2.17 2.17 2.19 2.16 2.14 2.19 2.24 2.22 2.22
## 2017 2.22 2.18 2.13 2.16 2.17 2.18 2.20 2.20 2.18
##
## $seasonal
## Jan Feb Mar Apr May
## 2003 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2004 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2005 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2006 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2007 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2008 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2009 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2010 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2011 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2012 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2013 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2014 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2015 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2016 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## 2017 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## Jun Jul Aug Sep Oct
## 2003 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2004 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2005 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2006 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2007 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2008 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2009 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2010 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2011 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2012 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2013 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2014 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2015 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2016 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## 2017 0.0061626221 0.0046470543 0.0012541972 -0.0097577076
## Nov Dec
## 2003 -0.0144005647 -0.0091029457
## 2004 -0.0144005647 -0.0091029457
## 2005 -0.0144005647 -0.0091029457
## 2006 -0.0144005647 -0.0091029457
## 2007 -0.0144005647 -0.0091029457
## 2008 -0.0144005647 -0.0091029457
## 2009 -0.0144005647 -0.0091029457
## 2010 -0.0144005647 -0.0091029457
## 2011 -0.0144005647 -0.0091029457
## 2012 -0.0144005647 -0.0091029457
## 2013 -0.0144005647 -0.0091029457
## 2014 -0.0144005647 -0.0091029457
## 2015 -0.0144005647 -0.0091029457
## 2016 -0.0144005647 -0.0091029457
## 2017
##
## $trend
## Jan Feb Mar Apr May Jun Jul
## 2003 NA NA NA NA NA NA 1.728750
## 2004 1.782500 1.788333 1.793333 1.795417 1.796667 1.799167 1.805417
## 2005 1.864583 1.870417 1.877500 1.885000 1.891667 1.899167 1.906250
## 2006 1.932083 1.931667 1.929167 1.930000 1.932500 1.931667 1.927917
## 2007 1.894167 1.887917 1.882500 1.874583 1.864583 1.856250 1.849583
## 2008 1.816250 1.815417 1.813750 1.811667 1.811250 1.809167 1.806250
## 2009 1.780000 1.775000 1.770000 1.764583 1.760417 1.757917 1.752917
## 2010 1.729167 1.724583 1.720417 1.717500 1.711667 1.704583 1.697083
## 2011 1.653333 1.646667 1.640417 1.632917 1.625833 1.620417 1.615833
## 2012 1.596250 1.595000 1.595417 1.596250 1.595417 1.593333 1.593750
## 2013 1.619583 1.624583 1.626667 1.627917 1.628750 1.629583 1.629583
## 2014 1.679167 1.697917 1.720417 1.747500 1.779167 1.812083 1.845417
## 2015 1.994167 2.008750 2.018333 2.025000 2.028333 2.029583 2.030417
## 2016 2.073333 2.080833 2.092500 2.108333 2.126667 2.145417 2.163333
## 2017 2.185833 2.190000 2.192083 NA NA NA NA
## Aug Sep Oct Nov Dec
## 2003 1.741667 1.752083 1.762500 1.772917 1.778333
## 2004 1.814167 1.825417 1.838750 1.850417 1.858750
## 2005 1.913750 1.921667 1.925417 1.926250 1.928750
## 2006 1.922917 1.921667 1.918750 1.910417 1.902083
## 2007 1.842917 1.830417 1.821250 1.820000 1.818333
## 2008 1.803750 1.800833 1.796667 1.790833 1.785000
## 2009 1.747083 1.744583 1.742917 1.738333 1.732917
## 2010 1.686667 1.676667 1.669583 1.665000 1.660000
## 2011 1.612500 1.608333 1.603750 1.600833 1.598750
## 2012 1.597500 1.600833 1.601667 1.604167 1.611250
## 2013 1.629167 1.634167 1.645417 1.656250 1.665833
## 2014 1.878750 1.909583 1.935833 1.958333 1.977500
## 2015 2.032083 2.034167 2.039583 2.050417 2.062917
## 2016 2.177083 2.183750 2.185417 2.185000 2.184583
## 2017 NA NA
##
## $random
## Jan Feb Mar Apr May
## 2003 NA NA NA NA NA
## 2004 0.0069898504 -0.0090815781 -0.0794089591 -0.0240151862 -0.0047844170
## 2005 0.0349065171 0.0088350885 0.0064243742 0.0364014805 0.0302155830
## 2006 0.0374065171 0.0575850885 0.0347577076 0.0014014805 -0.0006177503
## 2007 0.0253231838 0.0313350885 0.1214243742 -0.0531818529 -0.0227010836
## 2008 0.0332398504 0.0138350885 -0.0198256258 -0.0002651862 0.0106322497
## 2009 0.0394898504 0.0242517552 -0.0160756258 -0.0131818529 -0.0185344170
## 2010 0.0003231838 0.0246684219 0.0235077076 0.0039014805 -0.0497844170
## 2011 -0.0338434829 -0.0374149115 0.0035077076 0.0184848138 -0.0039510836
## 2012 -0.0167601496 -0.0257482448 -0.0114922924 0.0051514805 0.0064655830
## 2013 -0.0100934829 0.0046684219 -0.0227422924 -0.0265151862 0.0331322497
## 2014 -0.0796768162 -0.0686649115 0.0035077076 0.0039014805 -0.0072844170
## 2015 0.0153231838 0.0105017552 0.0555910409 0.0064014805 0.0035489164
## 2016 -0.0738434829 -0.0115815781 -0.0185756258 0.0530681471 0.0352155830
## 2017 0.0336565171 -0.0107482448 -0.0681589591 NA NA
## Jun Jul Aug Sep Oct
## 2003 NA 0.0166029457 0.0270791361 0.0176743742 0.0403529457
## 2004 0.0146707112 -0.0000637210 0.0345791361 -0.0156589591 -0.0258970543
## 2005 -0.0153292888 -0.0308970543 0.0049958028 -0.0119089591 -0.0325637210
## 2006 0.0021707112 -0.0225637210 -0.0441708639 -0.0319089591 0.0141029457
## 2007 -0.0324126221 -0.0242303877 -0.0341708639 -0.0006589591 -0.0183970543
## 2008 -0.0053292888 -0.0108970543 0.0149958028 -0.0210756258 0.0061862790
## 2009 -0.0140792888 -0.0175637210 0.0116624695 -0.0248256258 -0.0100637210
## 2010 -0.0107459554 -0.0017303877 0.0020791361 0.0130910409 0.0232696123
## 2011 -0.0065792888 -0.0004803877 -0.0037541972 0.0114243742 -0.0208970543
## 2012 -0.0094959554 -0.0083970543 0.0112458028 0.0289243742 -0.0088137210
## 2013 0.0642540446 0.0457696123 0.0095791361 0.0155910409 -0.0425637210
## 2014 0.0017540446 0.0299362790 0.0099958028 0.0301743742 0.0270196123
## 2015 -0.0157459554 0.0449362790 0.0066624695 -0.0144089591 0.0032696123
## 2016 0.0384207112 -0.0079803877 -0.0383375305 0.0160077076 0.0574362790
## 2017 NA NA NA NA
## Nov Dec
## 2003 0.0314838980 0.0307696123
## 2004 -0.0260161020 -0.0096470543
## 2005 -0.0218494353 0.0203529457
## 2006 0.0139838980 0.0070196123
## 2007 -0.0055994353 0.0007696123
## 2008 0.0135672314 -0.0058970543
## 2009 0.0360672314 0.0161862790
## 2010 0.0094005647 0.0191029457
## 2011 0.0135672314 0.0103529457
## 2012 -0.0197661020 -0.0221470543
## 2013 -0.0618494353 -0.0667303877
## 2014 0.0360672314 0.0116029457
## 2015 -0.0560161020 -0.0438137210
## 2016 0.0494005647 0.0445196123
## 2017
##
## $figure
## [1] 0.0005101496 0.0007482448 0.0060756258 0.0085985195 0.0081177503
## [6] 0.0061626221 0.0046470543 0.0012541972 -0.0097577076 -0.0028529457
## [11] -0.0144005647 -0.0091029457
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"plot(decompose(IRate))
Comparing two time series data URATE(Unemployment Rate) and IRate(Inflation Rate) in scatter plot:
plot(URATE,IRate)
Comparing two time series data URATE(Unemployment Rate) and IRate(Inflation Rate) along with time in time series plot:
ts.plot(IRate, URATE, col=c("blue","Red"))
Adjusting the time period from 1947 to 2003:
URATE1<-ts(UNEMP$UNRATE,start=c(2003,1), end=c(2017,9),freq=12)
ts.plot(IRate, URATE1, col=c("blue","Red"))
ts.plot(IRate, URATE1, col=c("blue","red"),xlab="Year", ylab="Percent", main = "Comparision of Unemployment Vs. Inflation in Time Series")
legend("topright", legend = c("Inflation Rate","Unemployment Rate"), fill=c("blue","red" ),bty="n",lty=c(1,1),text.font = 6, cex=0.64)