The Japanese people have a long tradition of national pride and a strong work ethic. These factors will combine together to turn around the Japanese economy. The people of Japan have faced many challenges, but they always manage to create something that demands pride, both from within and without their borders.
The demand for many Japanese products, such as electronics, is down. Many other economies in the world still have not fully recovered. Even the Chinese economy is showing signs of slowing down. With the demand for Japanese products, and demand for resources to build Japanese products, it's not likely their economy will recover in 2013.
There are too many problems in the world economy right now that make this question impossible. The US and Europe economies are still a challenge and there are still weakness in Japans GDP, its not a question if its going to recover in 2013, its going to be when is it going to recover?
Japan faces too many economic headwinds right now. The difficulties in Europe and the U.S. and the slowdown in the developing world will combine with Japan's strong currency and broken political system to ensure continued weakness. Unfortunately, demographic trends will exacerbate the problems. However, Japan's overall GDP understates the well-being of its people, because the shrinking population means that per capita GDP is rising.
With much of the world economy still very slow, including much of Europe and the US, it is unlikely that Japan will turn it around in 2013. Economic recoveries often take several years and to think that 2013 will be enough time for Japan is very optimistic. Especially with the world economy dragging down demand for cars and electronic goods, Japan should struggle in 2013.