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 4.14% per annum.
- FCX price at the close of July 25, 2024 was $44.53 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 76.19% per annum.
- FCX price at the close of July 25, 2024 was lower than the bottom border of the secondary price channel by $2.72 (5.75%). This indicates a possible reversal in the secondary trend direction.
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 FCX 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: January 6, 2021
End date: March 27, 2024
a = 3.4704
b = 0.0001
s = 0.1319
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 4.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1319) – 1
= 69.48%
January 6, 2021 calculations
Top border of price channel:
Exp(Y365)
= Exp(a + b × X365 + 2 × s)
= Exp(a + b × 530 + 2 × s)
= Exp(3.4704 + 0.0001 × 530 + 2 × 0.1319)
= Exp(3.7931)
= $44.39
Bottom border of price channel:
Exp(Y365)
= Exp(a + b × X365 – 2 × s)
= Exp(a + b × 530 – 2 × s)
= Exp(3.4704 + 0.0001 × 530 – 2 × 0.1319)
= Exp(3.2656)
= $26.19
March 27, 2024 calculations
Top border of price channel:
Exp(Y1,175)
= Exp(a + b × X1,175 + 2 × s)
= Exp(a + b × 1,706 + 2 × s)
= Exp(3.4704 + 0.0001 × 1,706 + 2 × 0.1319)
= Exp(3.9238)
= $50.59
Bottom border of price channel:
Exp(Y1,175)
= Exp(a + b × X1,175 – 2 × s)
= Exp(a + b × 1,706 – 2 × s)
= Exp(3.4704 + 0.0001 × 1,706 – 2 × 0.1319)
= Exp(3.3963)
= $29.85
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 4.14% per annum.
- FCX price at the close of July 25, 2024 was $44.53 and was inside the primary price channel.
Secondary Trend
Start date: September 21, 2023
End date: July 16, 2024
a = 1.1535
b = 0.0016
s = 0.0658
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 76.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0658) – 1
= 30.10%
September 21, 2023 calculations
Top border of price channel:
Exp(Y1,046)
= Exp(a + b × X1,046 + 2 × s)
= Exp(a + b × 1,518 + 2 × s)
= Exp(1.1535 + 0.0016 × 1,518 + 2 × 0.0658)
= Exp(3.6406)
= $38.12
Bottom border of price channel:
Exp(Y1,046)
= Exp(a + b × X1,046 – 2 × s)
= Exp(a + b × 1,518 – 2 × s)
= Exp(1.1535 + 0.0016 × 1,518 – 2 × 0.0658)
= Exp(3.3775)
= $29.30
July 16, 2024 calculations
Top border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 + 2 × s)
= Exp(a + b × 1,817 + 2 × s)
= Exp(1.1535 + 0.0016 × 1,817 + 2 × 0.0658)
= Exp(4.1046)
= $60.62
Bottom border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 – 2 × s)
= Exp(a + b × 1,817 – 2 × s)
= Exp(1.1535 + 0.0016 × 1,817 – 2 × 0.0658)
= Exp(3.8415)
= $46.59
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 76.19% per annum.
- FCX price at the close of July 25, 2024 was lower than the bottom border of the secondary price channel by $2.72 (5.75%). This indicates a possible reversal in the secondary trend direction.
- 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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