Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 39.63% per annum.
- AMGN price at the close of May 17, 2024 was $312.47 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 993.46% per annum.
- AMGN price at the close of May 17, 2024 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of AMGN price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: February 22, 2023
End date: February 26, 2024
a = 4.0939
b = 0.0009
s = 0.0529
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 39.63%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0529) – 1
= 23.56%
February 22, 2023 calculations
Top border of price channel:
Exp(Y947)
= Exp(a + b × X947 + 2 × s)
= Exp(a + b × 1,374 + 2 × s)
= Exp(4.0939 + 0.0009 × 1,374 + 2 × 0.0529)
= Exp(5.4565)
= $234.27
Bottom border of price channel:
Exp(Y947)
= Exp(a + b × X947 – 2 × s)
= Exp(a + b × 1,374 – 2 × s)
= Exp(4.0939 + 0.0009 × 1,374 – 2 × 0.0529)
= Exp(5.2449)
= $189.59
February 26, 2024 calculations
Top border of price channel:
Exp(Y1,200)
= Exp(a + b × X1,200 + 2 × s)
= Exp(a + b × 1,743 + 2 × s)
= Exp(4.0939 + 0.0009 × 1,743 + 2 × 0.0529)
= Exp(5.7940)
= $328.31
Bottom border of price channel:
Exp(Y1,200)
= Exp(a + b × X1,200 – 2 × s)
= Exp(a + b × 1,743 – 2 × s)
= Exp(4.0939 + 0.0009 × 1,743 – 2 × 0.0529)
= Exp(5.5824)
= $265.70
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 39.63% per annum.
- AMGN price at the close of May 17, 2024 was $312.47 and was inside the primary price channel.
Secondary Trend
Start date: April 15, 2024
End date: May 17, 2024
a = -6.1945
b = 0.0066
s = 0.0253
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0066) – 1
= 993.46%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0253) – 1
= 10.66%
April 15, 2024 calculations
Top border of price channel:
Exp(Y1,234)
= Exp(a + b × X1,234 + 2 × s)
= Exp(a + b × 1,792 + 2 × s)
= Exp(-6.1945 + 0.0066 × 1,792 + 2 × 0.0253)
= Exp(5.5996)
= $270.31
Bottom border of price channel:
Exp(Y1,234)
= Exp(a + b × X1,234 – 2 × s)
= Exp(a + b × 1,792 – 2 × s)
= Exp(-6.1945 + 0.0066 × 1,792 – 2 × 0.0253)
= Exp(5.4982)
= $244.26
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(-6.1945 + 0.0066 × 1,824 + 2 × 0.0253)
= Exp(5.8093)
= $333.38
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(-6.1945 + 0.0066 × 1,824 – 2 × 0.0253)
= Exp(5.7080)
= $301.25
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 993.46% per annum.
- AMGN price at the close of May 17, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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