The year of your arrival in Germany as well as the year of your departure are somewhat unusual if you arrive or leave at some point during the year. Such a split income and tax year will typically require you to file a tax return as your taxes are always calculated based on your full annual and worldwide income. The good news is that you always have access to 12 months of full tax credits and all the benefits as if you had been in the country for the full year. The bad news is that you will also have to report income for the part of the year you were outside of Germany. Your income during the time outside of Germany will not be taxed in Germany, but it will have an effect on the tax rate you pay on your income earned while in Germany.
The rule of thumb is: if your income before or after your stay in Germany is at a lower level than your income in Germany in your arrival or departure year, then you will qualify for a German tax refund. If it is higher, you will have to pay extra in Germany.