Biblically, the beginning of the year is the month of Nissan, which makes Adar the last month of the Biblical year.  In Rav Shimshon Pincus's sefer on Purim, he discusses the idea of 'mishenichnas Adar marbim b'simcha.'  What is it about this particular month that evokes happiness?  Rav Pincus attempts to explain why this time of year is favorable to Klal Yisroel, such that Our Sages recommended it as a time of good portent - suggesting that even if one has a difficult legal case, it is best to adjudicate it in Adar, as the outcome will probably be favorable  (Taanis 29a).   Rav Pincus contends that a root of happiness is found in novelty.  Everyone loves something new and fresh; it catches our attention and brings pleasure; the new breaks monotony and results in a rush of excitement.   

            While Adar is the twelfth and last month of the Biblical year, it does not symbolize hischadshus (renewal), in and of itself; however, the story of Purim - which is celebrated in Adar - is replete with hischadshus.   The majority of Jews in Persia were so alienated from Torah and its observance,  that they callously participated in Achashveirosh' feast - which ostensibly celebrated the destruction of the Bet HaMikdash.  The Jews joined their gentile captors in drinking from the holy vessels looted from a vanquished Jerusalem.   As a result, it was decreed that all of the Jews in Persia would be eradicated.  Through the intervention of Mordechai and Esther, a disaffected Jewish population was rallied, and as a result of sincere teshuva, Haman's horrific decree was nullified.  Not only did the Persian Jews survive, they reaffirmed their devotion to Hashem and Torah, and recommitted to accept and adhere to the tenets of the Written and Oral Law.  Through this turnaround, hischadshus is apparent in Purim.  The excitement and happiness of Purim can thus be understood, but the question still remains for the entire month of Adar.  To answer the question, the cycle of the year and its yomim tovim needs some further exploration.