The Arduino is generally used for sensing the environment and controlling simple devices. Which of those tasks would it be doing in your project?
how much data are you planning to send/receive per second?
in similar projects I would use the Arduino (or PIC24, dsPIC, PIC32) to sample real world data and transmit it (over serial communcations, WiFi, Ethernet, etc) to a Nerual Network ruuning on a PC which then displays the results
10 samples/second via serial line at 115200baud should be OKonce you get to 100s of samples per second you start to look at USB, ethernet or WiFi
an Arduino mega with a ATmega2560 has 8Kbytes of SRAM so you should be able to define three arrays of 100 elements of a basic data type such as int or float. What is the array data type?. what is the error message from the compiler?do you need to load 3 timeseries arrays of 10000 elements each at a time or could you send blcks of data for processingperhaps you should move to a Rassberry Pi