# Solved – Periodogram vs. spectral density diagram of a time series

Could someone explain to me the difference between a periodogram and spectral density diagram?

The first diagram is produced with this block of code:

``FF = abs(fft(datalist)/sqrt(128))^2 f = (0:63)/128 plot(f,FF[2:65],type="l",xlab="Frequenz",ylab="Spektrum") ``

and the second one with this code:

``x.spec<-spectrum(datalist,log=c("no")) ``

In both diagrams I have two peaks, which are clearly higher than the others, but in the first they are almost the same, but in the second (periodogram) the second peak is obviously higher than the first peak. Why are these two diagrams different?

In a periodogram, the first peak shows that we have something periodic in our time series, or second one or both of them? How can I interpret these two peaks?

EDIT

in the first diagram for the second peak:

``x=0.109375  y=36657.41193    x=0.1171875 y=36731.11184 ``

in the second diagram for the second peak:

``x=0.128  y=88176.01878  ``

and My Data:

471 379 484 479 527 548 576 534 443 375 475 514 516 527 445 403 487 382
510 451 562 569 575 528 450 351 467 504 505 520 441 407 460 421 504 475
569 555 575 516 460 359 460 496 492 529 490 465 410 460 475 509 549 564
571 515 375 392 458 450 488 510 459 475 410 514 496 563 550 572 539 396
388 491 447 471 515 454 467 363 499 486 522 583 567 543 459 370 437 500
483 529 451 408 463 395 511 468 559 551 576 527 418 380 471 496 494 515
453 415 454 431 503 490 575 564 571 512 400 371 484

Contents

There are many other ways to estimate the spectral density. In R `spectrum` call uses the same method that's in your first plot, but I think it additionally smoothes the data to achieve consistency