Yale Hirsch (publisher of The Stock Trader’s Almanac) devised the “January Barometer” in 1972, stating: “As goes January, so goes the year.” If stocks are up in the month of January, it’s usually going to be a good year for the stock market. Some people use the first five trading days of January for the “January barometer.”
 
There is as older weather-forecasting tradition that “as New Year’s Day (January 1) goes, so goes the year.”
 
 
Investopedia
January Barometer
A theory stating that the movement of the S&P 500 during the month of January sets the stock market’s direction for the year (as measured by the S&P 500). In other words, if the S&P 500 was up at the end of January compared to the beginning of the month, proponents would expect the stock market to rise during the rest of the year. 
 
If an investor believes in the ability of the January barometer to predict the equity market’s performance, he or she will only invest in the market in the years when the barometer predicts the market will rise, and stay out of the market when it forecasts a market pullback.
 
While the January barometer has been seen to produce better than 50% accuracy rates during 20-year periods, it is difficult to produce excess returns by using it since the improved performance by staying out of the market during bad times can be more than offset by larger losses incurred when the barometer incorrectly predicts a bull market. 
     
1 January 1935, Reno (NV) Evening Gazette, pg. 12, col. 2:
If the old maxim “as January 1, so goes the year” has any truth, Reno is to receive plenty of chilly weather in 1935.
 
1 January 1938, Oakland (CA) Tribune, “Tokyo Celebrates New Year Soberly,” pg. 4, col. 1:
This day of all 365 of the new year—according to a superstition—was the most important for “as New Year’s Day goes so goes the year.”
 
Google News Archive
17 January 1974, Rome (GA) News-Tribune, pg. 1B, cols. 1-4:
As January goes, so goes the year 
(...)
But of all probability patterns to be extracted from the historical data, “the January barometer beats all other indicators,” says Hirsch. “We doubt that any technique or indicator has been so remarkably accurate.”
   
15 January 1975, Long Beach (CA) Press-Telegram, “January Barometer is a consistent performer” by Sylvia Porter, pg. C13, col. 7:
As January goes, so goes the stock market for the rest of the year! This is the so-called January Barometer, and as Yale Hirsh (sic), a stock market analyst who has closely studied this forecasting tool, says, “It’s just incredible how the January Barometer has consistently predicted the annual course of the stock market over the past 25 years.”
 
Based on whether the Standard & Poor’s composite index is up or down in January, it is a fact that the market for the entire year has followed suit in 21 out of 25 years—an 84 per cent batting average that would be exciting even for a short span of time but which is nothing short of extraordinary over a full quarter-century.
 
In Hirsh’s words, in his just published ‘The 1975 Stock Trader’s Almanac” (Hirsh, Old Tappan, N.J. 07675, $9.95), “We know of no other indicator or market analyst that comes within a country mile of matching the january Barometer’s forecasting record.” The nine bear market years since 1950 were all preceded by inferior Januarys. The top 13 Januarys had gains of over 1 per cent and launched the best market years of the period.
 
18 January 1976, New York (NY) Times, “The Winds of January on Wall Street” by John H. Allen, pg. 110:
As January goes, so goes the year.
 
This little maxim has a lot of appeal in Wall Street these days, for the tremendous surge in stock prices early in the new year makes it almost impossible to see January winding up with a loss for the month.
 
Google Books
Stock Market Rules:
70 of the Most Widely Held Investment Axioms Explained, Examined, and Exposed
By Michael D. Sheimo
Published by McGraw-Hill Professional
1999
Pg. 234:
Still others believe the month of January is the great market forecaster. As goes January, so goes the year.
 
Google Books
The Complete Idiot’s Guide to Market Timing
By Scott Barrie
Published by Alpha Books
2003
Pg. 148:
Instead of waiting for the entire month of January to pass by, a little trick it to watch the first five days of the month. As we now know, as “goes January, so goes the year!” But, remember five days is a very brief period of time and major events can sidetrack this indicator as it did in 1986 and 1998.
 
Google Books
Buy the Rumor, Sell the Fact:
85 Maxims of Wall Street and What They Really Mean
By Michael Maiello
Published by McGraw-Hill Professional
2004
Pg. 153:
As January Goes, So Goes the Year
 
25 December 2005, New York (NY) Times, “All Eyes On January, And History” by Conrad De Aenlle, pg. B6:
“As January goes, so goes the year,: said Louise Yamada of Louise Yamada Technical Research Advisors, articulating a popular maxim.
 
She offered an analytical tool that supports the notion—“our own little January barometer,” as she called it. If there is a cumulative increase in the popular stock averages in the first five trading days of January and a further climb through the end of the month, “there is a 94 percent chance of the market being up for the year,” Ms. Yamada said.
 
Google Books
Stock Trader’s Almanac 2008
By Jeffrey A. Hirsch and Yale Hirsch
Hoboken, NJ: John Wiley and Sons
2007
Pg. 16:
THE INCREDIBLE JANUARY BAROMETER (DEVISED 1972):
ONLY FIVE SIGNIFICANT ERRORS IN 57 YEARS
Devised by Yale Hirsch in 1972, our January barometer states that as the S&P goes in January, so goes the year, The indicator has registered only five major errors since 1950 for a 91.2% accuracy ratio.
(...)
AS JANUARY GOES, SO GOES THE YEAR