options ls=76;   ** Demos  Nenana.sas  **; 
* Ice breakup time in Tanana River near Nenana, 
Alaska - for years residents have bet on the 
breakup time, which is considered the unofficial
start of spring. 
A wooden tripod is used to measure the breakup. 
More information is available at 

http://fairbanks-alaska.com/nenana.htm
 ; 
Data Ice; input year 1-4 mon $ 8-10 day 12-13; 
month = 5; if mon="Apr" then month=4; 
break = MDY(month,day,1960); 
*23456789 123456789 123456789; 
cards; 
1917   Apr 30  11:30 a.m. 
1918   May 11   9:33 a.m. 
1919   May  3   2:33 p.m. 
1920   May 11  10:45 a.m. 
1921   May 11   6:42 a.m. 
1922   May 12   1:20 p.m. 
1923   May  9   2:00 a.m. 
1924   May 11   3:10 p.m. 
1925   May  7   6:32 p.m. 
1926   Apr 26   4:03 p.m. 
1927   May 12   5:42 a.m. 
1928   May  6   4:25 p.m. 
1929   May  5   3:41 p.m. 
1930   May  8   7:03 p.m. 
1931   May 10   9:23 a.m. 
1932   May  1  10:15 a.m. 
1933   May  8   7:30 p.m. 
1934   Apr 30   2:07 p.m. 
1935   May 15   1:32 p.m. 
1936   Apr 30  12:58 p.m. 
1937   May 12   8:04 p.m. 
1938   May  6   8:14 p.m. 
1939   Apr 29   1:26 p.m. 
1940   Apr 20   3:27 p.m. 
1941   May  3   1:50 a.m. 
1942   Apr 30   1:28 p.m. 
1943   Apr 28   7:22 p.m. 
1944   May  4   2:08 p.m. 
1945   May 16   9:41 a.m. 
1946   May  5   4:40 p.m. 
1947   May  3   5:53 p.m. 
1948   May 13  11:13 a.m. 
1949   May 14  12:39 p.m. 
1950   May  6   4:14 p.m. 
1951   Apr 30   5:54 p.m. 
1952   May 12   5:04 p.m. 
1953   Apr 29   3:54 p.m. 
1954   May  6   6:01 p.m. 
1955   May  9   2:13 p.m. 
1956   May  1  11:24 p.m. 
1957   May  5   9:30 a.m. 
1958   Apr 29   2:56 p.m. 
1959   May  8  11:26 a.m. 
1960   May  2   7:12 p.m. 
1961   May  5  11:31 p.m. 
1962   May 12  11:23 p.m. 
1963   May  5   6:25 p.m. 
1964   May 20  11:41 a.m. 
1965   May  7   7:01 p.m. 
1966   May  8  12:11 p.m. 
1967   May  4  11:55 a.m. 
1968   May  8   9:26 a.m. 
1969   Apr 28  12:28 p.m. 
1970   May  4  10:37 a.m. 
1971   May  8   9:31 p.m. 
1972   May 10  11:56 a.m. 
1973   May  4  11:59 a.m. 
1974   May  6   3:44 p.m. 
1975   May 10   1:49 p.m. 
1976   May  2  10:51 a.m. 
1977   May  6  12:46 p.m. 
1978   Apr 30   3:18 p.m. 
1979   Apr 30   6:16 p.m. 
1980   Apr 29   1:16 p.m. 
1981   Apr 30   6:44 p.m. 
1982   May 10   5:36 p.m. 
1983   Apr 29   6:37 p.m. 
1984   May  9   3:33 p.m. 
1985   May 11   2:36 p.m. 
1986   May  8  10:50 p.m. 
1987   May  5   3:11 p.m. 
1988   Apr 27   9:15 a.m. 
1989   May  1   8:14 p.m. 
1990   Apr 24   5:19 p.m. 
1991   May  1   12:04 a.m. 
1992   May 14   6:28 a.m. 
1993   Apr 23   1:01 p.m. 
1994   Apr 29  11:01 p.m. 
1995   Apr 26   1:22 p.m. 
1996   May  5  12:32 p.m. 
1997   Apr 30  10:28 a.m. 
1998   Apr 20   4:54 p.m. 
1999   Apr 29   9:47 p.m. 
2000   May  1  10:47 a.m. 
2001   May  8   1:00 p.m.
2002   May  7   9:27 p.m.
2003   Apr 29   6:22 p.m.
2004   Apr 24   2:16 p.m.
2005   Apr 28  12:01 p.m.
2006   May  2   5:29 p.m.
2007   Apr 27   3:47 p.m.
   ;
%let yr0=1967;  
data dates; do year=1917 to 2020; 
ramp=(year-&yr0)*(year>&yr0); output; end; 
data all; merge Ice dates; by year;
proc arima data=all; 
i var=break crosscor=(ramp) noprint ;
e input=(ramp) /*q=(5,6,10)*/ plot ml;
f lead=5 id=year out=out1; run;
proc gplot; 
plot (break u95 l95 forecast)*year/overlay href=&yr0;
title h=1 "Ramp starts after &yr0"; 
title2 "Tanana River Ice Breakup";
symbol1 v=dot i=join c=black; 
symbol2 v=none i=join l=2 c=gray r=2; 
symbol3 v=none i=join c=gray; 
run; 

** Optional: Using NLIN to estimate ramp start point **; 
proc nlin data=all; 
parms C=1960 a=126 b=-.2 ; 
  X = (year-C)*(year>c); 
model break = a + b*X; 
run;quit;